One of the reasons that a 50cc Honda will produce enough power is that they use 4-stroke engines rather than the 2-strokes which Vespa etc have always used. 4-stroke engines tend to produce much more bottom-end power and are more economical than 2-strokes. They are also usually much more reliable at starting.

Virtually all cars, and most of the more powerful motor-bikes use 4-stroke engines for these reasons.