We did the Caribbean Explorer years ago and it was a great trip, but unless it has been remodeled since then, the boat was a little cramped and tired but we had a lot of fun. We flew to St. Martin and crossed to St. Kitts. We had some bad weather at St. Kitts and I got very seasick during the crossing. The diving at St. Kitts wasn't great but it may have been due to the poor vis from the weather.
The weather turned great and we crossed over to Saba and did most of our diving there. It was lovely Caribbean reef diving around the sea mounts and we enjoyed it. We also had the opportunity to do some land excursions on St. Martin, St. Kitts, and Saba, during that trip and that was fun.
Our cabin on the Caribbean Explorer was small and we had an ensuite toilet (and sink?) but we had to share the shower room with other guests. Again I don't know what the current situation is for cabins and accommodations. I remember that the food was good and plentiful and the dive staff and crew were great.
We have done 2 LOB trips to the Turks and Caicos, a Peter Hughes boat long ago and the Aggressor more recently, but we saw the T&C Explorer boat out on the reefs during the more recent Aggressor trip. It is a very large boat and it looked nice and roomy. The only negative that I've read about it is that the boat has a tendency to swing at anchor so if you miss it when trying to reboard you should just wait until it swings back toward you. Again I have never been on the boat so I can't comment - but I wouldn't hesitate to take another Explorer trip.
The diving in the T&Cs is better than Saba and St. Kitts in my opinion but the reefs start a little deeper, usually the top of the wall is about 60 feet. You will see a lot of big stuff in the T&Cs including sharks and rays. The corals aren't as nice as some other areas of the Caribbean IMO but they are still very nice walls.
Both of those destinations are good LOB trips because they are not easy places to visit. You can fly to St. Martin easy enough but then you would need to fly or ferry to St. Kitts and Saba to dive those islands.
It's easy to fly to Provo in the T&Cs, but the best diving are on longish boat trips from Provo so you can spend much of the day in boats to do some dives. With a LOB you can spend most of the trip around French Caye and West Caicos and enjoy the better sites at your convenience. We spent some time on land in Provo before boarding and Grace Bay Beach is gorgeous and we had fun, but it is an expensive destination.
Both of those regions were hit by hurricanes in 2017 and I haven't visited either since then so I don't know much about the recovery, but it sounds like they are making good progress.
There may be a lot of storms in the Caribbean in September - or it may be sunny and perfect! The water will be warm anyway and that is especially important for the T&Cs (IMO) because the water gets cold in that area of the Atlantic in the winter and spring. You should plan to buy trip insurance and DAN diving insurance, especially if you will traveling in the Caribbean in the fall.
I think that they would both be great trips at an excellent price and I would be happy with either, but I think you will get a nicer boat and better diving (at a higher price) in the T&Cs. Good luck with your decision!
