Both places offer some great diving.
Cozumel has great wall and drift diving. It is fabulous to just sit back and let the current carry you along as you take in the sights. The dives as a whole can be a little deeper 65-85 feet on the first dive of the day but we did all of our certification and first open water dives in Coz. The wildlife we have seen in Coz has been impressive including turtles, rays and a lot of fish, and more.
Belize is different diving. We dove Ambergris Caye over Christmas and really enjoyed it as well. The coral formations are spur and groove dives (like fingers) and typically runs shallower than in Coz 45-65ft - though you can certainly go deeper. Again the diving had a lot of life on them including sharks, rays, turtles, and more. Our preferred diving in Belize was off of the atolls - Lighthouse Reef, Half Moon Caye. The Blue Hole in Belize is definitely an advanced, deep dive requiring experience.