They are such different places, both topside and diving, it depends what your priorities are and what you want to see.
If the whole fancy big resort experience with mainstream restaurants and nightlife is what you really want for this trip, Hawaii is more likely to suit you. The convenience to dive ops and other things is going to vary depending on the island and where you stay, but it's not going to be nearly as convenient as a dive oriented place in Belize or a liveaboard either place. For example a lot of dive ops on the Big Island leave from Kailua-Kona, which is a longish (and often congested) commute from most of the really cool looking resorts you'll probably be interested in, so you need to watch out for that. (If you have the time I think a week on the Kona Aggressor and a week on land dedicated to other stuff is the best way to go. And FWIW, the food on the Kona Aggressor a few years ago was actually better than most if not all of the restaurants we ate at, including the expensive ones, go figure.)
Much more likely to see a whale shark in Belize, but mostly in specific days of certain months in a certain location, you really have to arrange your trip around it. Whales, varies with time of year but you have decent odds in Hawaii. Winter is when the humpbacks are there and June is way past peak season though, but you could get lucky. We were in the water with a pilot whale in August.
When you say you are stuck between Hawaii or Belize, what does that mean? Something about plane tickets or just somehow you've narrowed it down to those. There are places where you could do the resort thing and compromise less on the diving. Grand Cayman and Curacao come to mind.
