Not sure what you mean concerning "high rotation engines providing extra power". Factors influencing would indeed be the size of the engine in displacement, thermal efficiency, and propeller efficiency. Whether or not the engine is capable of high rpms doesnt figure in all that much, because to spin the prop too fast is going to cause a lot of issues, up to and including the propeller blades departing the aircraft. The larger the prop diameter, the slower you want the propeller rpm because of the tip speed. Look at the B29 for example. 4 big engines turning 4 really big 4 bladed propellers, yet at cruise speed, the prop rpm is about 400.
A good recip engine is going to be designed to get the max out of the engine at somewhere around 2500-3500 rpm and the reduction gears will depend on the diameter of the propeller. The pitch of the propeller also has a big role to play. A fine pitch setting allows you to run up to takeoff, then as the aircraft heads to and reaches its cruising altitude, the pitch is progressively changed to a more coarse setting, taking a bigger bite and allowing slower engine speed, fuel economy ard range. Advances in propeller technology, such as variable pitch and constant speed propellers have also helped.