It really depends on what you want, but I honestly don't think that you would be disappointed with either choice.
The diving at the two locations are both great, but very different. In Cozumel, you will primarily be doing drift diving. It is extremely relaxing and you just literally go with the flow. If you see something that catches your eye, it can be a challenge to try to get back to it.
In Grand Turk, it will pretty much all be wall diving. The wall is only about 100 yards off shore, so the boat rides are typically in the 5-10 minute (or less) range. TCI has a reputation for being very "sharky", but we only saw a pair of sharks one day in Grand Turk. We did, however see a lot of turtles. Grand Turk had a lot of life on their reefs, everything from tiny juvinile Cow Fish to Sting Rays, Groupers and as previously mentioned turtles. I was there in March, and the Humpback Whales were migrating through the area. While we didn't see any while diving, we heard their "whale song" on almost every dive. I stayed at a resort called
Bohio. It is a family run little place owned by a couple (Tom & Ginnie) of Canadian expats.
If you want some night life after hours, then Cozumel would be the better choice for you. Grand Turk is not known at all for its night life.
Personally, I liked Grand Turk better than I liked Cozumel, but ultimately, only you will know what suits you best. As I said though, I think both are terrific destinations. Have a great trip!