The most important factor in the diff is: you know what temperature the air that is cooking the beans "is", not so with a drum (or the drum skin temp).
Second, convection is a more efficient means of heat transfer, roasting the beans faster with lower heat.
In extremis: my roaster uses a max of 550 degs F and does a roast in 4 minutes (most Sivetz style roasters take longer with the same heat.)
Other advantages/disadvantages are more subjective, and up for debate.
I prefer roasting with air.