I have to confess I am currently running my Bryant with a chain. Further to the comments about getting the belt dialed in, I could never get it to stop creaking, despite reading & trying just about every possible thing that could affect it (belt tension, wheel alignment, greasing BB/crank interfaces etc). It was supposed to be a low-maintenance drivetrain but I spent far too much of my free time tweaking it. The IGH on the other hand is easy to set up.
The chain also allows me to run somewhat taller gearing (45/20) which suits me a little better, and with a chainguard (which the bike came with, even with a belt) I'm not losing much. I still love the bike - it's handsome, very practical and a great ride. I also knew the belt-drive was something of a gamble going in - but I still very much like the idea of having a frame designed with different drivetrains in mind in the way that the Bryant is.
ircclean's story about the sprocket is interesting. Having had the drivetrain apart on mine, ISTM the spline on the Alfine might be designed such that the sprocket breaks before the hub internals do in the event of too much torque. It basically has three fairly shallow rounded splines, rather than many square splines. It's possible that the alu Gates sprockets that worked great on a singlespeed hub with a conventional spline ran afoul of this on the Alfine hub.
I might give the belt another try when the CenterTrack stuff becomes more widely available - I kind of see CenterTrack as something of an admission that the first version of this system was flawed (especially combined with the materials change for the sprocket.)