On return to the USA, the first thing you notice when stepping outside the airport terminal is police cars. There are Massachusetts State Police, Transit Police, Department of Homeland Security Police, Federal Protective Service Police, and some other random police hanging around. It's not clear why they are there. Driving into town, there are more State Police hanging around the highways. There are local Police and more Transit Police. Getting into home, there are local city police everywhere.
It then strikes me that in Stockholm, police were always heard in some far off European-only siren wailing away. They were rarely seen in person, perhaps only a fleeting glimpse of a car rushing off somewhere. In reflecting back on the recent trip to Egypt, even the police weren't seen so much. I saw more military vehicles and people than police officers. This same thought occurs with trips to Poland, Sweden, Iceland, etc.
By contrast, visit Washington DC. There are so many overlapping layers of police everywhere it's not clear which police are responsible for which square centimeter of ground. I can't even name all of the different police departments I've seen recently in DC.
In the end, I'm not sure which countries are safer. The UN reports don't shed a clear picture, but what is clear is the USA is spending a lot of money on police and is generally in the top 10 nations for any definition of crime. Either the USA has much better reporting or just has more incidents. Even per capita we're 4x more European countries, as of 2012.
So many police everywhere is unsettling to most visitors. It's one of the first things they ask about "Is this number of police and sirens normal?" The answer is generally, "yes".