Do I have the following right?:-

Jet:-
Vx IAS stays the same as altitude gets higher.
Vy IAS reduces as altitude gets higher.
Both angle and rate of climb lessen as altitude increases.

Prop:-
Vx IAS increases as altitude gets higher.
Vy IAS reduces as altitude gets higher.
Both angle and rate of climb lessen as altitude increases.

If the above is right, is there a rule of thumb for how much the various
speeds change, or is it really aircraft+powerplant reliant?

TIA