Any time you get into physical combat things can get seriously ugly, see e.g. Eric Garner.
As for US vs. European statistics, you always need to make sure each is honest (e.g. are they counting all populations in their countries? Counterwise, remove the US south and we look rather European), and there's no question that the US is flatly more violent, e.g. remove all homicides with guns and our rate is still higher.
In addition, I know that you have to investigate before comparing what are ostensibly the same statistics coming from different countries.
I'm going to buy pepper spray soon, and I understood that it was basically nonlethal. I've been mugged a few times already, and I do believe it would have helped in at least one case (in which I absolutely would not have used a gun).
It can definitely kill, and I've read people have been charged for using it in what seemed to be legit self-defense. It's definitely force and not something to be used casually.
Even if the threshold is the same, that doesn't mean that the pepper spray isn't a much superior alternative, especially for people who are supposed to be protecting civilians, including civilians they're arresting.
Do you have a citation about the statistics becoming European if you remove the US south? This PDF breaks down police-related deaths by region:
http://www.bjs.gov/content/pub/pdf/ard0309st.pdf
And while the South is higher than other regions, the others are hardly what I'd call "low".
http://www.economist.com/news/leaders/21636033-united-states...
"American law enforcement is unusually lethal: even the partial numbers show that the police shot and killed at least 458 people last year. By comparison, those in England and Wales shot and killed no one."
I'm a HUGE proponent of nonlethal alternatives, I don't understand why there isn't massive funding for better tasers.