I think you must all be looking too deeply at this .... read my last answer!
The original question asked was why one of the identical aircraft ( with identical props ) gets off the ground quicker than the other. The fact that they both get off the ground with the same rpm is pretty much irrelevent ( at that given moment both will be delivering the same power ). I'd have thought it's obvious that a given rpm gives the same performance if the prop and a/c are the same .... just like my pushbike analogy with gearing and rpm.
What is different is accelleration! A more powerful engine will accellerate the aircraft to the given rpm in a shorter distance than the less powerful one .... so it gets off the ground more quickly.
Surely that answers the question!
IM