One big difference on shaft and belt driven cars are the motor position.
Shaft driven usually have the motor mounted along the main shaft and that may cause torque steering in one direction, it can however be helped with chassis tweak.
Driftcars may also be equipped with front oneway diff or oneway pulley (on belt driven) to create the effect of rear wheel breaking, like pulling the hand break to get the rear around.
Driftcars may also use spool instead of diff, it's ok to use spool in the front for on-road racing but not on rear axle.
Otherwise where should not be to much differers