100% Grand Cayman (especially if you are doing one of the Disney excursions). The Beach Break in Cozumel is PACKED with tons of people from many, many cruise ships-- the chairs are packed in rows like sardines on the beach.
7 mile in GC is nice, but my FAVORITE is (even though the travel there is long) Rum Point Beach! It is quiet, serene & every time I have been there (4) Disney has been the ONLY ship there. I LOVE THAT PLACE!