They both have great beaches. There is less to do in Grand Cayman, so I would spend the day there on the beach and do the snuba in Cozumel. Then once your snuba tour is over you can bar hop and shop in Cozumel...
But really its a tie on the beaches. You have the 7 mile beach on GC and lots of small beaches to pick from on Cozumel.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007