We dove Bahamas (New Providence/Nassau and Exuma) and Grand Cayman. As far as diving goes, I like Grand Cayman better. The Bahamas has alot of sand but lot's of sharks. I did not get to dive a wall off Long Island when there due to weather and at least that dive was touted as better. The "sand" dives were shallower and longer but life I found was sparse. Off Exuma at least there are blue holes to dive if that is what you like. I thought it was cool. There is a tugboat wreck in good shape.
The Bond wrecks I dove off New Providence were becomming piles of rubble so not great. As said before, the water can be cooler in the winter. We were there in early January with a cold front moving through all week. The air and water temps were 64F with high winds causing larger waves which did cancel few am dives. We stayed in Exuma later in the year and had much better surface and water temps. If I plan a winter trip I generally don't go to the Bahamas (once was enough) but you could get lucky and have great weather.
It can take longer to get to the outer islands (Exuma) however we did get a direct Miami to Exuma flight going in.
In Exuma there is the Thunderball grotto which I think can be at least snorkeled and there is a beach with swimming pigs. There didn't seem to be much else to do in Exuma but since we dove everyday I did not spend much time investigating. There were not alot of restaurants. I will say the beaches in Exuma was fantastic - better than GC's Seven Mile IMO. We did stay at Sandals but dove with an outside dive op since Sandals diving kinda sucks. The outside dive op - Dive Exuma- was expensive (like $180/two tanks). Per their website they now charge $140.
There are alot of islands in the Bahamas and I've only been to two. If you like the Bahamas do alot of research on the different islands.
Grand Cayman diving was better IMO with closer walls, tongue/groove reefs and we did dive stingray city. We used Don Foster's at the time but it's been quite some time since we've been there. There was quite a bit to do there - lot's of restaurants, Seven Mile beach, turtle farm, we went to Hell to send a postcard, and took a trip across the sound to see Barefoot Man play (not sure if he is still around or not) and walked around town shopping. I found Grand Cayman to be more expensive than the Bahamas in general especially for meals but the Bahamas was not cheap either.
If I had to choose, it would be Grand Cayman. You might look at locations further south in the winter for warmer weather and water temps. Unfortunately if you want alot of topside activities it usually means a higher population and probably cruise ships so secluded but beautiful islands have less topside offerings (aside from natural attractions).