Smoother running. Can be set up for countersteer drift easier for drifters.
Needs constant attention and replacement.
Lasts forever. Little to zero maintenance required.
Cons are opposite of belt pros really.
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Shaft drives have what is known as "torque twist," because their motors are typically mounted in-line with the chassis, whereas belt drives have their motors mounted transverse. It usually manifests itself in higher-performance chassis, where a lot of power is available. Belt drives do not exhibit this.
They also have what is known as "backlash," which comes from the play within the gears in the differentials. This manifests itself when going from forward to reverse or vice-versa, and sometimes when accelerating from a dead stop.
If you are going to be running on filthy surfaces, belt-drives will suffer damage easier than shaft drives, which can happily run on filthy surfaces without complaint.
Belt drives have an efficiency that is superior to shaft drives, and typically run longer than a shaft drive, if the same size battery is used (but only minutely).