Rich,
OK. Here is the rundown of a typical Aggressor day. This would be simialr for both Cayman and Belize.
Day 1 - arrive, check in, unpack, set up gear, meet people, eat, ...
Day 2-6 - breakfast, dive deck orientation, dive #1, snack (baked goods), dive #2, lunch (boat moves to new spot), dive #3, snack (savory), dive #4, dinner, dive #5 (night dive), hot chocolate
Day 7 - Only dive in AM (2 dives) - go back to port. PM open (in Belize, a group of us went cave tubing). Cocktail party in early evening, dinner on your own (although the captain opten sets up a group dinner in town).
Day 8 - get kicked off the boat by 8 AM so crew can prepare for next group.
Both Cayman and Belize boats are similar designs and vintage. Cabins a little small for 2 people, so pack light (as you are an experienced liveaboard diver, you know this, but I am writing this for lurkers too.) Bottom bunk queen size, top twin, so if you are a couple you can use the top bunk for storage. The crew will put your big dive bag into storage for the week, so it will not get in your way.
The rest of my comments are specific to Belize, since I do not know the crew of the Cayman boat.
There were no real pelagics in Belize (and i do not remember many in cayman either). As I said, the 'big stuff" was one manta, many spotted eagle rays. The walls of lighthouse reef are superb - in good shape (dive sites have permanent moorings - no anchors). My memory of Cayman is slightly faded, but I believe you will not be disappointed in Lighthouse Reef (particularly off half Moon caye). We did 24 dives on Lighthouse Reef (14 off long Caye and 10 off Half Moon Caye) and 2 off Turneffe island (no real wall, just a long reef slope). Good shallows, including some sandy areas to chase small rays, watch sand tilefish, ...
Many people took Nitrox course - the work is "self paced" and was done between dives. The cost of nitrox is $100 for the entire week, and if you take the course, they give you a discount. My advice - take the course at your LDS, and get a referral to do the Nitrox checkout on the Aggressor - why spend any time studying? (of course, if you can find an SSI course, there is NO requirement for a checkout dive - even easier - that's what I did). Having said that, people who took the course did not seem to mind the time - it was not a huge imposition. If you do want to do most of the dives, I urge you to take a Nitrox course somewhere - it makes a huge difference both in bottom time and safety margin (assuming you are not a scuba commando)
I honestly don't think you can go wrong with either choice. The crew of belize is very relaxed, friendly. The boat rules are max depth of 110' (except for Blue Hole), but it is honor system. If you do Nitrox, that limits your depth to 110 to 132 anyway (you will learn about oxygen toxicity in the course). The Blue Hole is the only "led dive". Everything else is self directed (you can always go with the divemaster if you want - I did to help find some tunnels that were not obvious.
If you go to Belize, take some good quality dark chocolate for Caroline - she will be ecstatic! Tell her I (Joel Jakubson) told you!
Final advice - go to the Aggressor web site, and read the Captain's Log archives for both Belize and Cayman - that will give you a flavor for what they have been diving.
Reply back with more questions,
Cheers,