I am from Italy and we have crippling corruption and criminality problems, even though we have a fifth of the population in 0.03 times the land area. I am familiar with the problems that scare tourists away :)
I would only like to point out that you quote terrorism and sexual assault as things comparable to your own police force abusing power over your citizens. I think there are a few important differences.
That being said, unless you live in a high crime area, you are unlikely to have much if any interaction with the police at all.
And when you do, it will likely be friendly.
Basing your decision on a fear of police abuse is like people who don't swim in the ocean because they are afraid of shark attacks.
People are scarred of coming to the US because of a few square blocks of Chicago and random improbable terror.
Cops there seem to have way too much power, and a worrying amount of them make use of it with enough regularity that there is never shortage of news regarding it.
Things are crap in Europe too, but it hardly ever gets that bad here.