As others have said, both have their pluses and minuses. Blackbeards is about the cheapest cost-per-dive you can get for diving by boat in a Caribbean climate. My son and I both really like diving, but both of us felt that it kind of started to feel like work -- especially on the days with 4-5 dives, with bells for breakfast early and then on-off with the wetsuit and gear, bells for dive briefings, wolf down lunch and dinner in cramped spaces, etc. Not really much time for a nap or activities -- hardly time to get dry before the next dive, and don't want to lay on your bunk wet. We're both glad we did the trip, and would not rule out another trip, but we're in no hurry to go again soon. If we do go again, I'm going to give myself permission to skip a few dives to relax a bit more.
We went to Cozumel for a week about 3 months after our Blackbeards trip. We had 5 days of 2 tank diving, and added a couple of night dives (which were great). We did some morning dives, and some afternoon dives where we could sleep in a bit. The diving was better in Cozumel, and we had more time to relax and do other activities (and enjoy some great Mexican food at different restaurants). I think in general this type of trip is much more to our liking, but everyone is different.