Fraoula,
I visited Patmos a few years ago. I only stayed two nights, and only really had one full day there so I didn't see all of the island.
I didn't think it was vastly different to other small greek islands. At the place where John is thought to have written the book of Revelation, there is a plaque on a wall and not much else to see. There is a tiny monastery but it was closed when I visited. The island is on the cruise-ship trail so there is a great long quay to accommodate them and there are a lot of tourist shops in the village, but most of the time things are pretty quiet. I found one sandy beach (forgotten its name) a long way from the village. There are infrequent buses half way to it. There is supposed to be a boat service to it, but it wasn't running when I was there due to the winds. Also, it was uncomfortable because of the wind and although I was told it was nudist, it wasn't, so I didn't stay long. There were, however, some secluded coves (pebble and shingle) along the way, with several people sunbathing nude.
I don't know whether this helps, but it's what I know.
I have passed through Sfakia (or Chora Sfakion, literally the capital of Sfakia) twice, changing from boat to coach or coach to taxi, so I know very little of it.
Greecemad.