I have seen plenty of European cities and some American ones, I don't see much of a difference in terms of urban vs suburban between the two. The main difference coming to mind is that, as European cities, towns and villages have far longer histories than American (or Australian) ones, there are stronger separate identities - for instance, people living in some place 30 miles from downtown Paris or London, which has long since become to all extents and purposes a suburb of the big city, may still see themselves as citizens of their own town, not Parisians or Londoners. My own hometown is no more than 15 miles from the centre of Brussels, but historically it has an old rivalry with Brussels, and just because Brussels is now more than ten times as big, doesn't mean that that rivalry stops or that the town sees itself as a Brussels suburb.

In a few cases, what you get is one big metropolitan area that isn't dominated by any single city - the Ruhr region in Germany is the best example, it's one of the biggest "cities" in Germany, but it's actually four or five mid-sized cities plus a ton of small ones combined. The Netherlands has something similar where both of their capitals, Amsterdam and The Hague, as well as Rotterdam and a bunch of smaller cities, are arguably all one big metropolitan area.