I've used both.
I was an early adopter and took a chance with the first generation (pre center-trac) belt/cog designs. In general, I LOVED it for grimy, slushy, wet conditions and had no desire to use a chain. I later sold that bike after accepting the fact that the geometry was all wrong for me, and went back to a regular chain/IGH.
For my current environment - essentially high desert and rocky mountains - with less than 12" of rain/snow per year, I'm fine with my chain. If I lived in a wetter climate - particularly with snow - I'd have no hesitation using a belt.
Either one with an IGH is a far better choice (IMO of course) than a derailleur when the snow begins to fall. Here's a shot of my current drive train (chain/IGH) after a relatively short 12 mile jaunt on snowy roads in near zero (F) temperatures. It ran smooth as can be. I've seen people (including myself) cursing their derailleurs on days like that.
