My $0.02...
Of the 3 I've only been to the T&C (T&C Aggressor this past August). As mentioned by others, almost exclusively wall diving. The top of the walls is somewhat deep (on average 45-50 feet), so safety stops are generally spent mid-water (and with long mooring lines and wind conditions, the boats really swing while moored). I really enjoyed the T&C Aggressor crew...they seem to have a consistently strong reputation. Lots of shark action. Not much to do topside except lay on the beach. Some of the diving you do on the liveaboard is on the same sites visited by Provo dayboats (mainly West Caicos). French Cay (where the best diving is) is almost exclusively by liveaboard.
I was looking at GC before I booked this trip and came to the same conclusion re: Little Cayman (it would be great to spend the whole week there...and the Aggressor sometimes does not make the trip). There are some great places to stay on LC (Little Cayman Beach Resort, Southern Cross Club, Pirates Point...each with their own unique vibe), although you probably won't get the same volume of diving in for your $ as you will on a liveabord. Re: land-based....there doesn't appear to be much to do there except dive and relax.....which is what I prefer. Sounds like the top of the walls are generally shallower at least on LC....maybe 20 feet.
My own personal conclusion: I want to try a land-based LC trip for my next trip. If you had to choose a liveaboard....to me, hard to beat the T&C...and there are 2 choices with strong reputations (Explorer and Aggressor).
Chris