I would like to know whether the APU of modern commercial airliners consumes more or less fuel than a jet engine. Of course, this will vary between aircraft types, so what comparisons in fuel usage are there on a modern jet such as a B737 or A320? What is the ratio between an engine hourly fuel consumption and the APU hourly consumption?
To give a comparison with an engine at idle:
The engines can use about 850 lb/hr at idle, which from those figures is about 1/10 of fuel flow at full (takeoff) power. So the engines use about 4 times as much fuel (each) as the APU does to just provide power. Of course these values will vary based on ambient conditions and the load placed on the systems (like the bleed air system).
This is why if a plane has to stop away from the gate for a while, they will shut down the engines and run on the APU.
The APU consumes less fuel because it doesn't have to contribute thrust to the airframe.
Many APUs have the same generator capacity as a propulsion engine. But they don't produce thrust. They can run at an optimum RPM for the generator requirements.
On a short flight each main engine might consume an average of 1260 kg/hour.