There's isn't necessarily more of either poverty or crime in USA cities than rural areas, it's roughly the same on average. (per capita; there are of course more people total in a city than a similarly sized rural area). Googling for cites, I find numbers all over the place.

I don't know how to compare problems between the USA and Japan, or decide what kinds of problems are "worse"... but our misperceptions of the size of various problems based on our "common sense" probably doesn't help.