Belt is efficient, low cost, and depending how belt tension is addressed - no or minimal maintenance. A good fit for many riders today. A proper design can handle high torque loads.
Shaft is more expensive, requires a bit of minimal maintenance (oil change, long haul), and can change the chassis dynamics slightly. Shaftie bearings don't necessarily last forever, but some of that may be due to people (esp. rain riders) skipping oil changes.
Chain is more maintenance than many today will bother with (I recall one post about a rider at a coffee shop speaking to a couple because he was concerned about the RUST on their chain. The lady thanked him, then turned to hubby and said - "Time we got the spray out". He pulls out a can of WD40 :shocked: and proceeds to spray their motorcycle chain).
Chain does have he advantage of allowing you to change the overall drive ratio on a bike, should you be inclined to raise/lower operating RPM of the engine at a given road speed.
My lazy man's solution to chain maintenance is to use Dupont's Chain Saver spray. Good lube, and is designed to be virtually self cleaning - works as claimed, at least in a street application where I ride.
Rgds, D.