There are three established dive ops on CC - Belize Diving Services, Frenchies and Big Fish. The first of these is a very professional organisation.
For atoll trips Frenchies and Big Fish have "big" boats though neither compares with the boat(s) used by AquaDives on Ambergris Caye, who stop by prior arrangement. They have a booking office on CC, and unlike all CC operators offer nitrox. To those who are qualified I recommend the use of nitrox (usually 32%, though 36% and indeed any mix is available if requested at least a day in advance) on either or both of the two dives that follow the BH dive.
My personal preference on CC would be to dive locally with BDS and for atoll trips use AQD.