I've been on the Sun Dancer in Belize a few times, and once on the Cayman Aggressor (as well as many land-based Cayman trips.) Both are good trips, but if you haven't done either yet I might choose Belize first. A liveaboard is a really good way to dive in Belize, as they go out to the atolls where the best diving is and hang out there for the week. People staying on land pay a premium and have a long boat trip to get out there for just one day at a time. There's also a lot to do on land in Belize, so if you have more than a week you could combine the liveaboard with a stay at a jungle lodge and do ruins, caves, etc.
People seem to have mixed feelings about liveaboard in Cayman because you can get to the same sites from land. Also because people usually want to get to Little Cayman, and the Aggressor doesn't always make the crossing if they judge conditions to be unsuitable. I still think it's a good trip - I for one enjoy the convenience of a liveaboard even if I can dive the same sites from land. I also think we got to spend more time on better sites overall by liveaboard than we do land-based. (Partly this is because you can simply get more dives in.) And if the weather cooperates it is an easy way of diving all 3 islands. Since Cayman tends to be expensive in general, especially if you're eating out a lot and doing lots of boat dives, the liveaboard might even work out to be a cost effective way of doing it.