Neither the US nor Europe has such a unified housing market that this could be a reliable statement. In Europe it differs greatly within countries, and there are many countries. In the US it also varies greatly within each state and there are many states.

Also at this point both have seen such negative upward trends in housing prices that the assumption that someone placed in the middle class owns a home at all (without any debt attached) is questionable. (But that's just a comment and besides the point)