As a frequent cruiser and diver, I second (or is it third) the recommendations for making your on plans. To me the financial benefit is secondary. My main concerns are small groups; freedom to change the dive plans and longer dives. In addition the cruise ship will frequently cancel dives for weather. My very first cruise in Grand Cayman this happened. I got off the boat, met my ride and had two awesome dives....its an Island, there is always a good side. I have seen this happen on several occasions. IMO the more experienced you are, the more you will want to get away from the "cattle boats" and enjoy the areas away from the "crushed" areas of the reef.
I will also pile on for the location comments. The most expensive shipboard dive I know of is in Belize. Either pay the cruise line or go do something different (Ziplines and cave tubing are options!). The logistics of a 30 min tender to the port, driving past the cruise ship to the dive sites and return (~3 hours total travel on water) doesn't make it feasible. The Ship's operator picks you up directly off the cruise ship and takes you to the atoll where their shop is. After dives they bring you directly back to the ship as well. HOWEVER, we only got a 35-40 min dive because of other divers running low on air. Second cruise there we didn't dive.