"America is a bit more dangerous in many places than Europe."
I'd be surprised if the most violent places and times in the US were really that different to the most violent places and times in Europe. However, what I suspect is different is where and when violence is likely to occur.
You should qualify that by where you live. There are dangerous places and there are safer places. America is a bit more dangerous in many places than Europe.
I wouldn't let my wife walk alone at any time in India these days but I have no problem with her walking alone in Beijing in the middle of the night.
The world is vast.