I am pretty convinced #1 and #2 are both true. POlice officers most of the times do not hunt down murderer or kidnappers (their is hardly murder in Europe, compared to the US), but are asked to appease husbands beating their wives, stop parties that are too loud, etc. Those people will hardly ever own a weapon - other then in the US.

Second, I am pretty sure there is another culture of violence and fighting with the police in the US. Car chases, for example, are way less often in Europe - criminals tend to give up, instead of fighting to death.