To me, it all depends upon how much time you have in port. If you are getting in early and have a FULL day, you would have enough time to do your own scuba excursion - however, if you are only in port for part of a day, I would recommend the ship excursion (even though it is going to be overpriced) -- just make sure to book early, as space is limited.
I did a very late booking (5 weeks in advance) and the dive excursions were all waitlisted, so I'm trying to find who Princess uses in Belize so I can contact them directly and try to make arrangements. I am an experienced diver and always carry my full gear.
If you are not a dive fanatic or don't own your own gear, don't worry about trying to bring your own. There is no discount offered when you provide your own gear