I've never been to Belize, but based on what I've heard it's much higher in crime than CR. Likewise the Caribbean coast of CR is much higher in crime than the rest, and there's been some infamous murder robberies of tourist there. More drugs too. There is a cultural reason for this that I won't go into. When I was in Limon, the main Caribbean city in CR there was young guys just "hangin out" watching me (and more importantly my backpack) constantly. I felt very uncomfortable there. Not that it's undoable. Just worse IMO. We did stay at a decent resort with my family on the Caribbean side of CR and it was fine, but near the larger towns there was notable presence of more scum than elsewhere in CR.
A friend of mine and his wife described the capital city of Belize by saying "we had to run into the shops to seek refuge from the thieves". After that and a few more similar accounts, I lost my desire to visit Belize.
Beisde, Belize was a disease ridden swamp. I suspect that's how the Brits got it. That no one wanted it. I like the mountains, so I think Costa Rica would be a better bet.