The main reason to go with a chain over a belt is suspension travel. Suspension travel is the bane of the belt drive. To get longer shocks with more travel, you need an idler pulley for the belt. This is because the belt will be tightest when the swingarm is parallel to the ground. As you move more away from that perfect parallel position, the belt gets looser and looser and looser, until it's so loose that it will jump teeth or shear teeth. A chain is much more forgiving! It is not supposed to be adjusted as tight as a belt... and if you do adjust it too tight, the chain will stretch pretty quickly. A too-tight belt will just roast your output shaft bearing. Or break, if you're lucky.
Chains are nice because you can easily modify the gearing too. You can technically do that with a belt, but only if someone actually makes pulleys in the size you want.
Charles.