If you're looking for a party, I'm sure you'll find it easily in both places.
I've never spent NY's in Coz or Playa, so can't give specific advice.
On Isla Mujeres (small island off Cancun, north of Cozumel), there is partying on the main square and all over (the very small) town with live music all night long, then everyone heads to the Eastern-most beach of the country to watch the first Mexican sunrise of the new year.
I would imagine it's kind of the same on Cozumel (dancing on the Plaza then driving to the East Side at sunrise), but you might want to ask confirmation by posting a thread in the Cozumel subforum.
Enjoy your trip !