[EricH]

Coasting isn't necessarily a problem. Sometimes, being able to coast into a particular location at the end of a match when the power turns off can make a big difference in the match. (OK, so you really meant cost...)

Chain: Easy to run, easy to adjust gear ratios, easy to tension. But, if a critical chain breaks, you could be spinning in circles on the field. If you're using #25 chain, extra care needs to be taken in alignment of the sprockets.

Direct drive: Chain/belt is still recommended for other wheels, and supporting the non-gearbox end of the axle is highly recommended. If something goes wrong in the gearbox, see what happens if you lose a critical chain. Saves some weight over a chain system, but is tougher to build right.

Belt: See chain. May be slightly tougher to do depending on method of joining belt ends, but is also reliable.

Gear: Heavy, but robust and reliable. If you go this route, you'll need tight manufacturing tolerances. +-1/4" isn't going to cut it, you'll need more like +-0.010" or better for best gear mesh/interface.

In terms of cost, chain/belt is probably the cheapest, followed by direct drive and gear.