I don't think this info is usually in the scope of most pilots. That's more up to the designers.
eg. The B737 will give pretty large pitch corrections in "speed on elevator" scenarios when you're outside of 10kts from the requested speed. But this is all relatively behind the scenes from the pilot perspective.
Pilots I fly with like to be smooth and so will often override the F/D or pick a smoother mode simply from experience rather than thinking of gain per se.