Is Europe safer than the US?

I'm not really talking about terrorism, but rather everyday violent crimes. I'm living in the US right now, and it happens all too often that children are getting abducted, policemen shot in my own city, or people murdered just going out on a hike (and this is just Iowa!). I lived in Norway last year, and this kind of crime was basically unheard of there. I have also spent some time in France and Spain and overall, I felt much safer there (for example, walking alone at night). These are just my experiences, and I know it is hard to generalize an entire country or continent. Just looking for some other people's opinions or experiences :) Thanks