Santorini is always on the top of my list. Parosand Naxoscompete for the second place. Crete follows the three islands. Although to completely explore Crete you need more time like at least a week or two. The beaches in the islands of Naxos and Paros are better than that of Santorini. 
You ride a ferry from Santorini to Paros and Naxos. These islands are good travel destinations beyond Santorini. 

At a Glance: 
Naxos or Paros
Paros and Naxos are both included in the top islands of Greece.
Paros and Naxos have excellent beaches although that of Naxos maybe a little bit better.
You can expect well-prepared local cuisine in each island’s restaurants. 
Naxos is a bit more ideal for families.
Partying and nightlife are more of Paros. It is also more urbanized with chic hotels and stores. 
Naxos vs. Paros
Rather than a competition, choosing which one of the islands you will visit depend on your travel  preferences and standards for your vacation. One travel itinerary maybe more interesting to someone but disliked by another. Expectations, interests and experience should all be considered for each traveler. 
Naxos and Paros have similarities and differences. 
Geographic Information and Other Details
Cyclades’ second largest island is Naxos. The third largest is Paros. Paros more of hills while Naxos is mountainous. Paros and Naxos both have wide land area and very nice beaches. Even if the land in both Paros and Naxos are fertile, more residents of Paros have turned into the tourism industry for work. Naxos still do have agriculture. Though as not as prevalent as before, residents of both islands are also into fishing and herding. 
Chora, town of Naxos
This town of Naxos has the major port and the amazing center of Naxos..

Navigating your way to Naxos and Paros
Naxos’ bustling hub is the town of Chora. Paros’ center is Parikia. Naoussa is also a hub of local life and day to day activities of Paros. Both towns have ports. Naoussa offers good views of the port, ruins of a Venetian castle and the arcs annd road of the old town of Naoussa It is also getting urbanized. Although  Parikia is more busy as Paros is the center of sea travel among the islands of Cyclades and receives plenty of ferries. The town of Naxos has a more local vibe than Parikia  as influenced by its geographical location and architectural designs. Parikia seems to be a gem that needs further discovery. Common features of Naxos and Paros are Cycladic architecture, the presence of old towns, Castro area, arcs and thin roads. There are nice beaches in both Naxos and Paros. 
Paros has a more convenient public transportation system than Naxos. Buses have trips from Parikia and Naossa early in the morning to the other corners of the island. This is particularly helpful when peak season comes in for travelers that wish to visit the beaches and villages. Naxos has more of a locally-oriented public transportation system. The early trips of buses start from the different corners of Naxos to Chora. Trips from Chora towards the other villages start in the afternoon. This schedule follows that of the residents’ routine but may not be of much benefit to travelers who wish to maximize their time through public transport. However, if you are going to Plaka, Agia Anna and Agios Prokopios there are available trips that connect these beaches to Chora. In some instances there are also trip to and from  the southern beaches towards Chora. 
You can rent cars to explore Naxos and Paros. Their roads are good. Due to its mountainous terrain, Naxos’ villages are scattered throughout the island. There is no travel loop you can follow. The roads in the west coast of Naxos are better as it is where most of the activities take place. As you go towards the center, you can observe more curves. To go to the east beaches and villages, you need to get past the Zas mountain and travel the opposite way. Curves are abundant in the east so you will encounter rough roads as you travel beyond the main towns. Naxos’ northern and southern parts have the same road system. While Paros has a flat landscape and the residential areas are situated in the coast. You can conveniently have a full-day tour of Paros. 
Naoussa and Parikia are connected to the closest beaches through water taxis 
Top Greek beaches are found in Paros and Naxos. Both are known for their beaches having fantastic sand. Golden Beach, Santa Maria and Punda are the bustling beaches of Paros. Also in Paros is the simple but emerging beauty, Molos. The nearby beach of Kalogiros, Glyfa and Tripiti are off-the-beaten thus you can enjoy it by yourself. Naxos, on the other hand, have Plaka, St. George Beach, Agia Anna and Agios Prokopios. The serene beaches of Naxos are Ayiassos, Aliki, Kastraki, Mikri Vigli and Pyrgaki. The nude beaches are Plaka in Naxos and Lagerri and Paros. 
You need a bit more research to get to unpopular beaches in Naxos. Psili Ammos, Kalandos, Hilia Vrisi and Pinelo are not that advertised even if they are as nice or of similar quality with their famous counterparts. In Paros, the residents endorse all of their beaches including the smallest ones like Lolandonis and Farangas. You can explore your hidden sanctuary in either islands as they have beaches and coves scattered around. 
Most villages of Naxos are situated inland rather than in the coast. Agia Anna and Agios Prokopios are located on the seaside but have become a little more touristy. Tourism has not reached most villages of Naxos. They particularly retained their local routine and culture. Villages situated inland kike Apiranthos, Filoti or Halki  receive a decent number of travelers. Apollonas also receive some guests but there are villages like Moutsouna or Lionas that still look like from 20 years ago. Tourists are completely rare to the villages od Potamia. While Koronos appears to have not aged any bit. 
Paros mostly have villages or towns situated in the coastal areas . Their accessibility and geographical location expose them to tourism.  Punda Beach is particularly touristic. Pisa Livadi and Pounda Antiparous are now being influenced by tourism as well. Aliki and Drios have simple and subtle tourism industry. Paros do have villages inland and the most known is Lefkes. This villlage is lovely, traditional, well taken care of and has been recently improved. Residents come back to arrange their houses into local style. Traditional bars, nice galleries and stores have also sprung up. 

Historical Attractions
Paros and Naxos have related history. Important artifacts have been previously found in both islands. Each has an ancient site and  an amazing archeological museum. These are meaningful attractions but not really much of a wow factor. The ancient site in Parikia are physically open while that of Naxos is not exposed. You can see both attractions for free. There are several ancient sites in Paros that can even be reached by signs like those in Kolybithres beach, Koukounaries Kamares village towards old Akropolis but expect that is not much to see. Naxos has the same situation although it has the lovely Portara. It also has sites spread throughout the island such as Temple of Demeter, old Iria, aqueduct and the various Kouros. 

Religious Places
Paros has the Ekantotapyliani church in Panayja which is very important to Greek Orthodox religion. Paros also have the elite Moni Logovardas (off limits to visitors) and the picturesque Moni tou Christou tou Dasous close to Petaloudes park (the nuns are congenial). Agios Joannis Chrisostomos is one of Naxos’ monasteries. It is very common in the Cycladic islands to have a lone church on top of a rock to at  least 2 small old churches built next to each other. These churches are ancient particularly those in the areas of Marmara, Marpissa and Prodromos. Naxos also have its own set of churches built as early as 6th century such as Panayia Drosiani. Naxos has preserved the original details of its churches and remained standing on its special areas. Paros, on the other hand restored its churches. Even  Panayia Ekantodapyliani looks modern though it was built in 3rd or 4th century by St. Constantine as per St. Heleni’s wishes, his mother.   
Water Sports and Related Activities
Naxos and Paros are popular windsurfing destinations. The beaches east of Naxos and west of Paros are similar in terms of the quality of the stream and strength of wind. Famous windsurfing spots in Naxos are Plaka and St. George. For Paros, good for windsurfing are Golden Beach and New Golden Beach. St. George also has waterskiing. Santa Maria and Kolibithres in Paros also have waterskiing. In Naxos, kitesurfing is in Punda. In Naxos, kitesurfing is in Mikri Vigla. Paros has diving centers in Santa Maria Beach while Naxos has facilities in Plaka and Agios Prokopios. In Naxos, horseriding can be done Agia Annam. In Paros, horseriding takes place in Naoussa. St. George and Parikia have sailing. Banana boats and kayaks are available for both islands. Hiking is also excellent in both islands. But Naxos has more hiking spots that Paros namelu climbing the Potamia and Zas Mountain. Paros do have the Vyzanine trail to Prodrommos from Lefkes. Signposts are available for this trail. There are also hiking routes to Drios from Logaras. Naxos only have tennis courts in 1 or 2 of its hotels. While in south of Parikia in Paros, there is the Agia Irene’s tennis club. 
Museums and art exhibits in Naxos and Paros
There are several museums of different themes found in Paros and Naxos. Benetos Skadas of Paros built a museum close to Aliki, housing miniatures of famous buildings, ancient objects and fishing boats. In Parikia, connected to  Panayia Ekatontapyliani, a museum holds a collection of relgious artifacts. Historical Byzantine items are housed in Agios Athanasios in Naoussa. At the same town, there is unassuming local folk museum that features local wardrobes. 
The Venetian Museum is located in the town of Naxos. Three types of small museums are found in Apiranthos- folk art, archeological and geological museums.
In terms of art galleries, the town of Naxos has Petalouda Art. In Paros, Naoussa has Medousa and Parikia has Apothiki.

Products made in Naxos or Paros
Naxos and Paros are popular producers of dairy. Naxos is known for producing various types of cheese such as feta, graveria, anthotiro and kefalotyri. Although less popular, equally excellent cheeses are made in Paros as well. Naxos and Paros are also producers of olives, olive oil and wines.
Naxos has a Kitron distellery located in Halki. Naoussa house one of the winery of Paros.
In Paros, Moraitis is an established brand of wine. Paros also make Souma, it is a homegrown alcohol drink with similarities with Tsipouro/Raki. Kitron is Naxos’ alcoholic product with at least two companies. Valindras is the most popular brand. Kitron has at least 3 flavors. Paros’ famous pastry brand is Hamilothoris. Naxos and Paros also produce other pastry products and desserts like jams, spoon desserts, loukoumades and amygdalota.  
Each year, Naxos produces huge amount of potatoes. 
Paros is a big producer of excellent quality chicken peas that are used as important ingredient for cooking in the whole island. 
Naxos and Paros are known for its local artistry. There workshops for pottery and artwork. Naxos has  Fish & Olive pottery and Paros has Yria Ceramics. 
Naxos and Paros are world famous for their emery and marble industries. Moutsouna and Lionas in Naxos still have the sites of the emery production. Visitors can also visit the marble quarries in Naxos and Paros. 
Day Tours
Santorini, Koufonisia/Iraklia and Mykonos/Delos are popular day tours from both Naxos and Paros. From Naxos, there is a complete guided travel on a bus. There is also a boat tour that features beach hopping around the island which is not present in Paros. Unlike Naxos, Paros has a tourist-friendly transportation system with beaches accessible to any vehicle. Paros do have boat tours to Despotiko and Antiparos. A bus tour is also available that run to the town of Antiparos.

Local cuisine
Food is guaranteed delicious. There are plenty of ingredients produced locally. Delicacies include mizithropitakia (little pies of mizithra) and  greek salad with xinomizithra. Paros’ favorite meal is dishes made of chick peas cooked in a traditional clay oven. While in Naxos, sun-dried gouna fish is a local favorite. 

Paros and Naxos have various kind of accommodations ranging from campsite to rental rooms, to moderate level hotels to luxurious hotels. Large full-service hotels are also available like Porto Paros and Naxos Imperial but these hotel complexes are few. And be mindful that despite the luxurious stay they want to portray, these hotels are still not of five-star levels unlike those in Crete, Mykonos and Santorini. Lodging in Paros and Naxos are more simple. Lodging in Paros is spread out. First class lodging is situated in Monastiri/Kolibithres beach close to Naoussa and Parasporos beach close to Parikia. In Naxos, first class lodging is at St. George Beach, Agios Prokopios and Stelida. Budget hotels are also found in St. George. In Paros, budget rooms, studios and small-scale bed and breakfasts are found in Parikia. Stay in Naxos is more affordable than Paros. Naxos also have studios equipped with kitchenette. Paros have seasonal villas and houses for rent targeted at moneyed-celebrities. A week stay in a full-service rented private house in Myti, close to Farangas, is priced as high as 25000 euros. 
Dining out or cooking
As large number of visitors flock to Paros and Naxos, supermarket giants such as Atlantic and DIA are available and more affordable than the local counterparts. Carrefour Marinopopoulos has a branch in Paros to. Naxos has its homegrown  Koutelieris that have quality products at fair prices. 

Locally produced fruits, vegetables, fish, meat, cheese and wine are of excellent quality and definitely worth the money.

Most of the hotels in both islands particularly the beachfront accommodations offer breakfast to tourists. There are breakfast diners along the beaches of both islands. An excellent find is Naxos town’ Rendez-Vous Café. 
Both islands have bars and restaurants that offer excellent food. There is a least one pub present each village. Naxos is in the more affordable range than Paros. 
Gyros and souvlaki places are found in both Naxos ans Paros as wells as places serving sandwiches, pizzas and crepes. Greece has a healthy homegrown fast food chain comparable to McDonald’s, Goody’s. There is  a branch in the town of Parikia. Previously Goody has a branch in Naxos Town but has ben closed for a while now, the only exception to the successful fast food chain’s history. 
There are Asian and Mexican restaurants on Naxos. While Paros has an excellent Thai restaurant. These are proof that other cuisines beyond the famous trattoria or pizza places are also present on these islands. 
Holiday in either Naxos or Paros won’t be complete without tasting their pastries. Pastry shops and bakeries are aplenty in both Naxos and Paros. These goodies are good snacks for travelers. Good dessert places include Naxos’ Waffle House and  Naoussa’s Hamilothoris Zaharoplastio. Naoussa also has in its alleys, Paradosiako, that offers loukoumades honey puffs.
Paros is a partying paradise with Parikia as the party capita followed by Naoussal. The party scene is active year-round. Naoussa is considered by foreign travelers as the island’s hotspot while Parikia is known as the nightlife paradise. Punda Beach also organizes different DJ performances and event aside from the fact that it has beach pubs, restaurants, swimming pools and shops. Some bars closes late during peak season such as Lefkes, Aliki, Druos and Piso Livadi. Naxos has more subtle nightlife. Naxos town has that bouzoukia places and some nightclubs. Events and performances are also hosted in the beaches of Plaka, Agia Anna, Agios Prokopios and Apollonas. Paros and Naxos are often filled up with tourists from mid-July until August 20. Naxos is more couple and family-oriented than Paros. Young travelers prefer Paros more so expect that nights can get wild and exciting.

Activities and Events
During the summer, Paros is busy with local celebrations and several events arranged by the local government. Naoussa has the Fish & Wine Fair for the first Sunday of July and the popular pirate night on August 23 and  Panayja is celebrating Ekatodapyliani on August 15. Paros Cultural Park Ai Giannis Detis serves as a venue for different recitals and events. Paros is along where the Aegean Sailing Rally takes place. Local and international celebrities commonly visit Paros. 
The Venetian Castle as a private institution hosts traditional Greek nights, concerts  and recitals. Summer is the season of celebrations in Naxos. There are also countryside concerts and exhibitions in Bazeos Tower. The Korono’s Agia Marina festival (July 17) and Apiranthos’ Agios Joannis (August 29) are just few of the island festivals that offer Greek dance and music on different dates and themes. Although Paros and Naxos are popular for their local musicians, Naxos is particularly famous for its excellent violinists.