The prime differences between European and American police are:
1) structural differences in that American police forces are semi-atonomous entities with poor command-control response down the chain (federal, state, county, city, town) whereas European police are basically all federal employees subject directly to central command and monitored as such, and
2) American police have a much longer history of dealing with, and adapting their policies to the governance of, high-violence subpopulations like (southern) Italians, the Irish, and Africans.