The one place where I've seen the most "big" sharks is the Maldives. I routinely lost count of the oceanic white/black tip sharks, usually in excess of 20 per dive, with quite frequent sightings of hammerheads, tigers, mako and other "serious" sharks. There were also innumerable turtles - my record for one dive was 7 very large ones.
In Belize we have all these types of sharks and I've seen them all, but not very often. Recent sightings at local dive sites include a hammerhead, a whale shark, several tigers, several bulls. Plus lots of nurse sharks - on one dive this morning probably in excess of 40. They come so close they brush against you.
The only place I've seen lots of hammerheads here is in the Blue Hole at around 250', when I was surrounded in three dimensions by a school of them - probably 15 or 20. But I've never heard of them getting up into recreational dive depths there.
Other than nurse sharks, I wouldn't recommend north Belize for predictable large shark encounters.