Honestly, I've been to SF and NYC (Manhattan only) and have barely seen any homeless people. It didn't look better or worse than a typical European city. Probably I just didn't go to the bad districts?
I didn't feel like a saw many more obviously homeless people in the parts of Manhattan or Brooklyn I was than I do in say Oslo or London, but I realize that that is only a small part of NYC.
I've never, ever heard anyone not wanting to go on public transport here because of homeless people shooting heroine in there. Unlike Californians among which this seems pretty popular