I was at Nachi Cocom and Chankanab a few weeks ago. They are both nice as far as sunbathing. NC has more "beach" where you can wade into the water. Chankanab offers more activites like dolphin discovery and the sea lion show as well a beautiful garden. Sorry I haven't been to Playa Palancar. You may want to check out www.cozumelinsider.com there is a beach chart with info plus links for more detailed info.
Chankanaab has really nice deep sand...the beach does not slope down into the water as there is a reef at the waters edge. Some stone steps lead down into the water and can be a bit slippery when wearing fins. It wasn't crowded when we were there but that was several years ago. It could accomodate a lot of people, plus there are changing rooms and lockers. There are places on the beach to buy snorkel gear and drinks, plus there is a nice restaurant there as well. There is a small museum, nature walks, dophin encounter and shops also within the park.
Sorry, I haven't been to the other places to compare.
Nachi Cocom will be far away quieter and with better service that the others. It is lovely and has a pool and wide sandy expanses. Really good day to relax. Chankanaab Park, Playa del Sol, and Mr. Sancho's will be too crowded.Have a good time in Cozumel!