Depending on where you are going in Belize, I wouldn't worry at all about theft. We were there 8 years ago and spent most of our time in the West in the mountains and really hardly saw any people besides fellow hotel guests, tour guides, and Mennonites.
If you're staying in Belize City, i would worry, but then I'd also ask why are you staying in Belize City. Ha.
Edit, to try and give some input to your question;
Really not super familiar with either Bushnell or Vortex's lineup, even despite having a legend m, all I can give is general advice. Make sure it is waterproof/purged. Even without rain it is so thickly humid in the jungles there. I know you mentioned 10x, but I think that's a mistake. There was only one occasion where we could see for more than a few hundred yards and that was when we climbed up onto an old ruin that broke through the canopy. Even then, atmospheric conditions with all the humidity made it very hazy. It is also very dim beneath the canopy so a bigger pupil diameter would be nice.
In general, something 7 or 8x, 400'+ fov, waterproof, 30-35mm min, and lightweight is what I'd want if we went back.