After being in that cesspool of a country called belize (4th stop), I would definitely go through Carnival for any excursions there. We had a third party cave tubing/ATV thing there, but they cancelled it due to heavy rains the week prior. I'm very happy with that due to seeing first hand the restless natives they had there and how pushy and in your face they were there after we decided to just walk around the city. we turned right around and drank at the wet lizard all day and I am not a big drinker either, but they were good.
I know the above sounds bad, but every place else, I always use third party excursions, unless Carnival's is cheaper.