Small airplanes with fixed pitch props...
At a constant RPM, best power mixture delivers more BHP, therefore more speed.
Economy mixture, less BHP, less speed.
Then we look at constant speed props on small (and large) piston powered aircraft.
A glance back to the days of the 4-engine piston-powered airliner will provide a clue about fuel economy.
These aircraft were cruised at (normally) a constant BHP (using BMEP recovery techniques) and the lowest RPM, within engine operating perameters, was used, to enhance engine longivity.
On smaller GA types (with constant speed props), generally speaking, the lowest RPM cruise allowed will normally provide the best fuel economy.