I was always lead to believe that belts are the most efficient means of transmitting power, followed closely by chain, but only when new, and then the shaft drive.
Belts that I have encountered have generally been heaps quieter than chains, and like shaft drives the no mess, is a huge plus. Low maintenance is also a big plus. Now huge horsepower presents a big problem to belts, also the use of belts on primary drives, like the ones used on Harley like setups, have problems too, as the clutch hub that the belt drives too, moves to disengage the clutch belts do not like side ways movement also they do not handle stones and other road debris.
However with these pitfalls I know of several Harley riders that the rear belt was original when the bikes were traded in, 1 with over 120 thousand miles on it. Not bad and yes he used to give the bike a hard time. Wish I could get that sort of life out of a chain.
Even when you sit back and work out the cost of belts, yes more expensive compared to a chain, and yes a pain in the butt to fit, if they last that long, it works out more cost effective than chains.