My Wife and I have had the pleasure of diving Grand Cayman, Little Cayman and Cozumel. Up front I must confess that we are very partial to Cozumel. Like Joe, we stay at Fiesta Americana Dive Resort and dive with Dive House(just a walk across the street from the hotel). We go there each May as our annual vacation. The hotel is away from the cruise ship pier and town(a $5 taxi ride). The diving is wonderful as the reef structure is very healthy. It is of course drift diving and that is why you may see more boats in the area of the dive sites than in Cayman(their's are mooring bouys, only one to a site, first come, first dive). From the dock of Dive House you are aproximately 30 minutes from the most popular sites and 45-60 minutes from the tip of the island and punta sur dive site. Dive House has the Experienced Diver Plan where computers and experience are required. Usually the boat has max 8-12 divers with plenty of room. The dive has lockers to store your gear(you clean your gear, which I prefer). There is plenty to do down town if that is your thing. You can party, shop, or just walk around in complete safety. Cozumel is one of the safest islands I know and the value of the dollar to pesos is great.
I would not go back to Grand Cayman because it is too commericalized for us. We like the laid back atmosphere the smaller islands have offer.
As for Little Cayaman, totally different from GC. We stayed at the Little Cayman Beach Resort, last October, and dove with Conch Club Divers. The Reef Divers dive shop are associated with LCBR but, they had some large groups and they had their boats booked up. This was to our advantage. Conch Club Diver owner, Bill Christofers, has a great dive operation. The max we had on our boat at any one time was 8(one day) and the rest of the time is was 4-6 divers. Little Cayman is a very small island with very little to do unless you like to tour the island(highly recommend) and snorkel the beautiful shore line. For the meals I recommend you do the meal packages as there are very few resturaunts on the island not associated with a dive resort. The meal at LCBR are 5 star and they will gourmet you to death with the desserts and entrees(notice I listed the desserts first). As for the diving, you do three tanks a day, two morning(before lunch) and one afternoon(after lunch). The diving is wonderful, totally different from drift diving. The Bloody Bay Wall is a site to behold. As to socialization, you always meet some wonderful people and make great friendships that hopefully will last forever. They have a central meeting area (THE BAR) where most everyone attends each night. Another thing to remember is the Caymanian dollar is stronger than the US dollar so it does cost more to go to the Cayman Islands. The only real draw back to us is getting to LC. The turboprop flight from GC to LC has a weight limit. Since we carry our dive gear, the 50lb weight restriction per person is a bummer. They do charge you for each lb over weight and some bags may not make it over unitl the next flight. Other than that I would return to LCBR and dive with Conch Club Divers tomorrow. (A tip: Our last full day on LC we did not dive because we had an early flight the next day. We packed our dive gear and sent it to the airport,LCBR takes care of this, and it went over that evening to GC when the flights were not full. This assured us that our heavy baggage would be able to depart GC with us. They still charge for the over weight and your baggage is held in a secure area for you to pick up when you arrive in GC).
We enjoy both places. It would be a hard choice. But, for the value of the trip, ease of getting to the island, and the value on the island, I have to pick Cozumel.
Hope this helps.
Burt