I would recommend diving both ports. However, if I could only dive one place, it would be Belize. Also, since this is your first ocean dive, I would recommend using the ship's dive op at Belize or Roatan so you do not have to worry or think about anything other than enjoying your dives. The ship vendors at both ports are excellent. Your ship vendor in Belize will probably be Hugh Parkey's dive op taking you to Turneffe Atoll, which I like better than Roatan's reefs for the most part. The advantage of taking the ship's op in Belize is they pick you up and drop you back at the ship so you do not have to deal with tendering which can be problematic if you are trying to join up with an off ship op. At Roatan, the ship's op is AKR which I have also have used, and have had excellent dives with them, so I can strongly recommend them as well. If you are going to dock at Mahogany Bay in Roatan, I can also highly recommend Barefoot Divers which has a dive departing at 1000 for cruise divers, and then you can have lunch and then take their afternoon dive for a two tank dive. A problem that I have found with February Caribbean cruises is the possibility of "a Norther" cold front/wind which can really screw up dive operations and cruise ship itineraries. I have been re-routed on more than one occasion, and trying to revise and reschedule dive reservations with off ship vendors can be very frustrating using the ship's erratic satellite based internet.
Hiring a private DM for your first two tank ocean dives is not a bad idea (but not critical), and can further reduce your stress and allow you to have maximum fun on your dives. Be sure to let the DMs know these are your first ocean dives so they can help you have the best dives possible.