I'm not an american, I actually live in Germany. And as long as you rent instead of buying hohsing affordability is okay in most cities, and in those where it isn't the transit network is good enough that you can easily commute without an expensive car.
Renting in the US also is very cheap outside of cities. You can rent in New Jersey and take the train into NYC, or rent in Vallejo and take the train into San Francisco. Over all the income/rent or mortgage ratio, in my experience having rented and purchased in both countries, is much more favorable in the US. Quality of life is a different story.
It was easier for me to find a rental in NYC than in was in Berlin so I wouldn't really say Germany is ahead there either. Maybe if you got a rental 10 years ago? German rental markets are price-controlled which means extreme shortages because... surprise surprise... Germans don't build either.