As far as I know Playa del Carmen is closer to the Capri then Cancun is- so you might want to go there.
Playa has various nice bars and discos to go to- main difference between Playa and Cancun would be the size of places I think.
So in case you are looking for huuuuuuge discos with hundreds of people going wild at foam parties or bikini-contests (like Daddy O's or similar- the other names just escaped my memory...) you might want to head to Cancun. Places in Playa are smaller- and more fun if you ask me. You could check out the Blue Parrot or the Tutix.
Not sure about nightlife in Cozumel- but one disadvantage is that the ferry does not run all night as far as I know (unless that has changed in the last years). Once spent one night there- didn't find it too exciting, but I might have been to the wrong places!!
Hope this helped...