Kinsey,
I've not been diving yet in Belize, but like you I've heard it's fabulous. They're often rated right with each other, with Coz coming out a bit ahead because of accessibility (it's cheaper to get there and stay there).
If it were me, I'd do anything I could to find a way to do both. However, if only one were truly doable, I'd look at the other options in both places - what to do that day? Is there something else in Belize you want to do? My understanding of the port is that it's NOT a good one to do independently without an arranged tour (either pre-arranged on your own or through the ship). Cozumel may be easier to do on the cheap - you could spend about $30 for the both of you and snorkel Chankanaab so still get some of the beauty, for example. But I'd decide it based on whichever port I'd feel most "deprived" (as in picking a much less attractive second choice) if I weren't diving. It's an odd way to choose, but helps me feel like I'm not missing out and stay upbeat regardless of my choice.
If you do want to try to stretch your budget, consider arranging your diving independently in Coz. That can save as much as 1/3 to 1/2 off the ship's excursion rate. If you need recommendations as to operations to contact yourself, let me know. I'd not arrange independently in Belize - I believe that's a tender port, and difficult logistically on your own.
Sure hope you can do both! I don't know about you, but I don't get near enough chances to go diving
