Without knowing the details of the statistics, I wonder if the disconnect between perception and statistics has to do with population distribution? I've lived in the suburbs of the US, as well as right in Manhattan. In the suburbs, many nights we wouldn't even lock the door. In Manhattan I was attacked by thugs with a knife in the subway.
I now live in Ankara, a city with an official population larger than Chicago, but I can walk 15 min from my home and be in the middle of a field with no signs of civilization for miles. I think nowhere else in the world has urban sprawl that comes anywhere close to what you find in America. So, if you want an accurate comparison, I think you'd have to isolate and remove the statistics from suburbs, as they essentially don't exist outside the US.
I now live in Ankara, a city with an official population larger than Chicago, but I can walk 15 min from my home and be in the middle of a field with no signs of civilization for miles. I think nowhere else in the world has urban sprawl that comes anywhere close to what you find in America. So, if you want an accurate comparison, I think you'd have to isolate and remove the statistics from suburbs, as they essentially don't exist outside the US.