If you're comparing two of the exact
same design types, differing only by displacement - then in this very specific instance displacement might help dictate which one is more powerful, but it's quite unlikely to be double the HP for twice the size even then.
The 50cc I believe qualifies as a small motor, the above two stroke examples could be the commonplace motorized bicycle two stroke kit motors (2hp) vs the 50cc Morini, KTM50 & their clones (9hp), of which are 4x the HP at a minimum vs their exact same displacement comparison.
A common small displacement four stroke example relevant to this application would be the 99cc Harbor Freight Predator vs the 49cc Honda CRF50 & clones, both of which are just about 3hp... despite doubling the displacement.
Displacement alone means very little in generality, pretty much limited to knowing which parts ya need to order, there's so many flavors even with common engine types - piston ported, case inducted, reeded or the flathead & OHV conundrum, the bore vs stroke ratio, compression ratio, the quality of manufacture... there's too many variables, just to many exceptions to list lol, let alone to trust a catchphrase
...as for landscaping equipment, give weedwackers & model airplane engines a google - similar in displacement, it's amazing what 14,000rpm+ can do