We've been on the T&C Aggressor for diving twice
nce in Sept 1996 and more recently in June 2004 (we also were on the TCA for the whale expedition in Feb of this year).
The current boat was put into service in 2004 and is terrific. Captain Piers is a "divers captain" -- that is, he is diver himself and is very accomodating to the needs and desires of his passengers. Assistant Captain Christopher is a great diver, great photographer, and a whole lot of fun. The rest of the crew is first rate, including the important job of chef. As just one example of how cooperative they are, in 2004 they accomodated our request for a dawn dive, even though that meant the crew had to get up extra early (and we still did the usual five other dives that day as well).
The diving we did in T&C doesn't feature much in the way of wreck diving (there used to be a very cool underwater sphere left over from a french tv show, but its gone now). Healthy reefs and varied fish life, including both "big" stuff (sharks, eagle rays, etc) and little stuff.
We were on the Cayman Aggressor in 2000 -- since then the boat, captain, and crew have all changed as I understand it. I've done a lot of Cayman diving over the years and, frankly, my preference is to do a land based GC/LC trip -- 10 days, 5 at Cobalt Coast in GC and 5 at Little Cayman Beach resort. The diving from the Cayman Aggressor is great, but you have to enure the crossing from GC to LC which can be rough (and sometimes can't be done at all or in a timeframe that allows much in the way of Bloody Bay Wall diving). Flying from GC to LC takes the worry out. By the way, wreck diving is not a major feature of Cayman diving either. There are some wrecks, but most are in the major falling apart stage to the best of my understanding.
Finally, as for Belize, my only experience is a land-based trip to Turneffe Island Lodge last year in late May. I did speak to some folks who were on the Aggressor and they seemed to have had a very nice time. Again, not a wreck-oriented dive.