I've been on the T&C Explorer II twice - once on their Turks & Caicos itinerary and once on their Bahamas itinerary (San Salvador and Conception Island). Both were fantastic trips, but I'd say the diving was definitely better in the Turks & Caicos, with two exceptions - we saw multiple hammerheads and had a minute-long interaction with a dolphin on the Bahamas trip. That aside, the reef was in much better shape in Turks & Caicos, and we had more interactions with pelagics - stingrays, reef sharks, and nurse sharks on almost every dive. We saw reef sharks in the Bahamas too, but not nearly as often. And very few stingrays or nurse sharks, for whatever reason. There's a green algae that was all over a number of our dive sites in the Bahamas. I don't remember anything like that in T&C. It wasn't a deal breaker, but definitely hurt the overall look of the reef.
Visability was terrific on both trips - maybe slightly better in T&C, but that nitpicking. We saw some lionfish on both trips, but neither location was completely overrun by them. Probably saw a few more in the Bahamas than in T&C.
I've never been on Aquacat, but I understand that it tours around the Exumas. From everything I've read, I get the sense that the diving in San Salvador and Conception is better than the Exumas, but don't know that for sure.
Hope that helps,
James