Karpathos or Kythira
 

So I've narrowed down my selections for my next trip to Greece, and they happen to be at opposite ends of the country. I'd love to hear from someone who has been to both islands. I have been to Greece three times to Patmos, Symi and Astypalea, all smaller islands with beautiful chorae. I'm attracted to the rugged beauty of Karpathos, particularly its beaches, but its main town doesn't look so great. I understand that beyond the main town (which is full of tourists) the island is very sleepy and traditional. While I would love to see that, I enjoyed the handful of fashionable shops, pretty architecture, and excellent food on the three islands I've visited so far. I like islands with a small, relaxed but stylish community of expats or transplants from Athens. It seems Kythira offers more of that. If the landscape and beaches are that much more staggeringly beautiful on Karpathos, I'd go there. Never having visited a greener Ionian island though, I might be equally impressed by Kythira. I wonder which island actually gets more tourists. Thoughts?

added: I saw a video of a boat unloading droves of people onto an already crowded beach - apella i think. Hopefully there are more options, but it seems like there are only a few sheltered spots on the east coast. I don't care how nice the beaches are. If it's that much more crowded on karpathos it would definitely steer me to kythira.

Neither Karpathos nor Kythira offer jewels like the choras of Astypalea or Symi.
Pigadia is rather ugly and noisy and not touristy (despite the many small hotels/hostels). There are no decent beaches.
By far not all Island beaches are crowded. The North with the very nice hill city Olympos and the beaches below (often rather long hikes) is a completely different world.
Kythira is popular with Greek tourists and never really crowded. The Chora and the beach at Kapsali (just below) are nice. There is also a good never crowded sandy beach at Diakofti, close to the ferry harbour (some B&B's and some restaurants, nothing else). Agia Pelagia is nice too.
Daily flights from Athens and daily ferries from Neapolis, twice weekly ferries from Piraeus and Kissamos/Crete.
https://www.greeka.com/greek-islands-guides.htm