Do not forget that most aircraft have different AT control laws, in more modern aircraft these are quite complex, yet generally they are all designed for the primary roles; take off mode, cruise (climb / descent), and precision approach.
In addition to the differences in aircraft characteristics, each AT will also behave differently for each flight mode. When using AT without the autopilot, most ATs may not operate as you expect / require for a manual approach. Those ATs that I have flown all tended to destabilise the aircraft, making the approach pitch control just a little more sensitive, which in turn makes the speed oscillate.
Above all else, do not try to help or over-ride an automatic system, sooner rather than later it will bite back – in a big way. If you do not like the performance of an automatic system, then disengage it and take over manually. Treat autos like co-pilots if you don’t like what they are doing take over … if you don’t like what the Captain is doing … speak up.
“An autopilot is like a co-pilot, but never learns”.
“A co pilot is like an autopilot, but makes mistakes”. (Sorry co-pilots, you make mistakes in order to learn, and then you become Captains ... to make mistakes).