I had two accidents during my 5 years of commuting, and both times I only got minor scratches and had to replace my shoes. Both happened at speeds a determined bicycle rider could achieve, but I suspect I wouldn't be as well protected on a bicycle (both the machine itself and the protective gear tend to be much lighter there than on a moped). If I needed to do that again, I'd buy a model with two wheels at the front, which would have prevented both accidents - though I'm not sure if added stability wouldn't encourage me to ride faster.
So it's pretty specific, but if you're somewhere where driving culture is not too cutthroat, the roads can support single-track vehicles, and the traffic rather than actual distance is the limiting factor - owning a bike can be an objectively better option.