Anecdotally, among myself and my friends we have more stories of problems with theft and encounters with hostile people from very brief travels to Europe than all time spent on public transport in the USA. To be fair, I haven’t lived in NYC where public transport is famously more dangerous.
I also suspect that foreigners are more targeted for wallet thefts while traveling in Europe.
However, watching multiple friends get pickpocketed on European public transport and having to shake some sketchy people who were being aggressive with women in our group during our brief travels shattered my illusions that European public transport is universally superior in safety.
Edit to add: I also thought it was funny when we met up with someone’s friend in a populous European city who refused to ride public transportation with us. He would drive his car from point to point and meet up with us at the destination. He seemed to believe that the underground was not something people his age liked and was surprised we were riding it without a second thought.