The APU has more power on most aircraft than you would ever believe
I believe an APU has the same power as listed in its brochure, usually something between 50 and 90kvA depending on the aircraft.
At some point in
every aircraft towing operation I was in control of, the pilot would say "aircraft is yours". This is because I was outside and able to see backwards, with direct comms to the tug driver, and they were upstairs with limited vision and no way of talking or signalling the tuggy, save for jamming the brakes on and shearing the tow pin.
When I finished, I gave control back to the pilot.
When I have control, I'm responsible for not crashing the plane into something - a fact the pilot is pretty glad about on the ground!