Timing belts are great, no doubt, but if you put them on your drive train and though your match to match use will work out well, look at it over the entire tournament. As your days go on the belts wear down and eventually run the risk of stretching. A place of high use in your robot like your drive train is not the greatest location for a timing belt. Drive trains simply go under too much stress too frequently to balance out the pluses and minuses of timing belts. A better example of a good use of a timing belt would be like tyeing your shooter wheel to your motor.
For the record, motorcycles use Timing Belts and Chains, sport bikes generally have chains whereas cruisers usually have belts.
BTW while researching to find what type of chains bikes generally use, I stumbled across a
very interesting article.