[Jnadke]

I don't think those are belts, the pulleys are drawn too narrow. Those are chains & sprockets.

Depending on the belt, chains and belts are nearly identical in the concept and function. The difference is that chains are typically more durable and can transfer more torque. If you use v-belts, they usually can transmit a certain amount of torque before they slip (slide without rotating the pulley), which would be a good thing if you have a very high-geared robot and you don't want the breakers tripping.

Other than being lighter and easier to assemble/dis-assemble, belts have no significant advantage over chains & sprockets. Of course there's the whole slip thing, which is good when you're dealing with combustion engines (stall = bad). On robots, however, we seem to like to stall our motors with all the pushing (since nobody has designed a true CVT, yet), so I guess this could be considered a bad thing.