Interesting read. I've experienced both worlds, and I think a lot of the violence in the US is the result of a weak state, or at least a state that directs its force in the wrong direction. There are no man-hunts or high-speed chases in Germany - because the government always knows more or less where you are (which makes it even less credible they didn't know about the NSU). Police don't use their guns much, because nobody else does, but also because they have many other ways of making your life miserable (ever heard of a yellow letter?).
When it comes to social mobility, we're no different from most other places - you need the right antecedents.
However, if you were poor before, you'll experience a relative improvement in Germany. You won't become socially respected, but you can get by and maybe even a job.
This leads to my anecdotal observation that many middle or upper-class immigrants feel more discriminated in Germany than lower-class migrants. In the US, your class privileges tend to migrate with you. You'd never see the son of a Kenyan senior government official just go and run Germany. Although we did have one chancellor who was allegedly raised in a barn, but he was an odd one.