I've dove Grand Cayman from shore and more recently the Turks/Caicos Explorer. Both are equally good wall diving. I personally think T/C was slightly better in terms of bigger pelagics. At French Cay and West Caicos we saw multiple sharks on every single dive. Equal numbers of turtles and sting rays. More Eagle Rays off Cayman's north wall. More turtles near the Turtle Farm. Smaller stuff, coral formations seemed about the same on either. Once you get out over a 6000' wall, it really doesn't matter much where it is. Maybe the coral was slightly more profuse off the Turks/Caicos. Some of that might be that West Caicos, French Cay and several other Caicos are also uninhabited so only visited by LOB's or dayboats from Provo. A lot of West Side Grand Cayman diving has suffered from the 50ish operators that dive it daily IMO.
You might consider Explorer instead of Aggressor also. The boats are configured differently - the advantages for us were that there's an extra public level on Explorer. They have a covered flybridge up top that has bench seating, tables and stocked drinks. I even slept up there a couple days. And most of the cabins on Explorer are main deck or the one above it. And have beds not bunks. If you're a couple, it's a queen bed. Our room had two single beds with storage underneath, a night stand, a desk in the corner and enough room to open the door. And two good sized windows. On Aggressor it's all double/triple bunks with portholes. All are one deck level down. With the flat screens in every room. Only 3 cabins are bunks on Explorer - one deck down.
I liked walking from my room to the dining room/lounge then out the door to the dive deck. Downside is that if you have a loud crowd (we did) they keep you up at night. Food was excellent although I'm sure it is on Aggressor also. Both boats do the same itinerary - at least twice during our trip I saw Aggressor nearby. At one site off West Caicos, I swam under it on the way back to our boat. All the moorings are close to shore with the wall farther out so both boats do similar dives. One unusual thing is that Explorer really swings on it's mooring. If you miss it, you wait for it to come around again 5mins. later. You almost can't catch it - I tried once.
I don't know which trip is clearly better. Maybe Cayman Aggressor if they make the run over to the Sisters because you've got the Tibbetts off Brac and Bloody Bay Wall off LC. The closest thing to a wreck we saw off T/C was a big diesel engine. And ThunderDome an abandoned set of structures used once to film a TV show. That failed because people were getting bent while playing. Sort of several big open domes in about 40-50' Boring....
But the Cayman crossing doesn't always happen - sometimes it's too rough. Mostly that seems to be in the Winter. Review some of their trip reports in their thread here because they comment when they couldn't. When that's the case, CA circumnavigates GC - many of the dives they do I've done off dayboats. Their last dive, Devils Grotto, we've done from shore in Georgetown harbor at Eden Rock. So then it becomes more convenience. (and price) I don't think you could do as many dives off Grand Cayman without more driving and a higher overall cost.
From a shore-based perspective both seemed equally pricey. And both have great beaches. More nightlife on Grand Cayman but not by much. From what I've read Both Sister Islands are really quiet. And Grand Turk when there's no cruise ships in port. That seemed to be daily in Georgetown on GC also - that was annoying since some of the dives are downtown/near downtown. Driving is on the other side and they don't look before stepping off the curb into traffic.
There's no shore diving off Provo - reef is about 500 yds. offshore at NW Point - the closest spot. I only spent two days and one night on Provo but it seemed more pleasant. Seven Mile Beach has been called little Miami Beach - areas can be pretty crowded. All the dive resorts are OK though, Cobalt Coast is too far north to be busy, Sunset House is south of Georgetown and the Reef or Ocean Frontiers/Compass Point are 45mins. drive east. Afaik the only dive resort in the Turks/Caicos is Bohol on Grand Turk. Both Islands have dive operators who will pick you up at most resorts and take you to their boats. And of course there's Stingray City on Grand Cayman. And now the Kittiwake.
One last thing is that both T/C boats follow the Humpbacks to the Silver Banks in winter. Those are snorkel only trips. So LOB diving there starts around the 1st week of April.
hth,