For some reason US has a higher homicide rate than Greece and most of Europe.
Only if you look at it a certain way. War is homicide, and Europe has had a LOT more of that than the US.
Although it has changed some, most European nations have a much more ...consistant culture than the US. More homogenous. Areas that don't have a high level of consistency in the culture are more violent. Look at the Balkans, for one example. Multiple ethnic groups (with the added complication of different religions), have been fighting and killing there for centuries. Europe has had nearly constant warfare between someone since the days when there were no nations, only tribes.
This year marks the 100th anniversary of the start of the First World War. Which, btw, was begun in Europe...
Europe is currently experiencing what I think is its longest continuous period of "peace" in centuries. (no, please don't mention ethnic cleansing in the Balkans..they don't want to count that against their peace) I hope it lasts a long, long time, but history argues against it.
the US is often referred to as a melting pot, and in many ways, it is true. The pot bubbles and roils, its not a calm simmer all the time. And if you look at the ideas put forth by many of our "leaders", it does seem true that the dross floats to the top....
Homicide for personal reasons, by individuals, the US has more than Europe, currently at any rate. Homicide for political reasons, by groups? Europe has a really good lock on that, the US can't even come close.