"air delivery will seem weaker in most cases because the APU compressor is much smaller than the engine compressor, the amount of air available for bleeding from the APU is less than engine, the delivery pressure from the APU is lower than the engine"
We should be careful not to simplify here. Bleed pressure can depend on rpm and demand. Engines have variable output depending on rpms and whether the high stage or intermediate/low stage is providing air. In contrast, the output of APUs these days is variable, depending on demand, despite rpms running at 100%. If there is only one pack running, the APU will output less bleed air than when, say 2 or 3 packs are running or during main engine start.
Are we talking about a specific aircraft?