To the OP-
The saying in drag racing "There's no replacement for displacement' is still valid for these, but we're working with much smaller engines and in order to really see the effect of a larger engine for this purpose, we need to look at the whole machine. As an example, the 17.5HP Briggs engine is .5 Liter. That's not much but there are ways to produce more torque- longer stroke, created by the crankshaft and using a smaller diameter piston for the same displacement. The crank is rotated by combustion in a larger circle, so we need to look at it as if someone had put a pipe on a wrench in order to increase torque- it's harder to rotate the crank with a shorter lever arm (smaller diameter of rotation).
Then, we need to look at the effect of the grass resisting the blade's rotation and this is why a sharp blade and correct mower speed are important- the blade is only sharpened close to the end and moving too fast causes the grass to pass the sharp edge, which just grabs and causes the engine to bog.
If you slow down, it will cut better. Extremely tall grass will require more than one pass with the deck set higher for the first.