In my experience cars are much more dangerous than public transport.
I've taken public transport my whole life, in numerous countries, and only bought a car for the first time 7 years ago when moving back to the US. Never had any incident on public transport or felt unsafe. Was it always as comfortable and convenient as my car? No, but that's a separate issue.
I'm a weekend road cyclist and I've had a number of very close calls with cars -- invariably big pick up trucks, sometimes flying an American flag (you know the type) -- purposely rev up and buzz by me as close as possible on small country roads, sometimes honking as well or flipping the bird out the window. Any little stumble or twitch at that point and there were a couple of times I would have been in the hospital or dead.
Yeah, there are sometimes strange people on public transport, as well as homeless, etc. But I've encountered more *holes driving cars than on the bus or subway.