I wonder if the difference is fundamentalism? If we suddenly changed every fundamentalist or evangelical into an atheist, would America look like Europe? Fundamentalism formed as a reaction against modernism. Apparently fundamentalism didn't gain as much traction in Europe, so Europeans were forced to confront modernism without the simple verities of fundamentalism as a defense. Belief is not so central to Catholicism and the more liturgical styles of Christianity, so they are not as threatened by modernism.
Here is a link to "The Fundamentals". Almost every point is a reaction to modernism IMO:
https://en.wikipedia.org/wiki/The_Fundamentals
I think there's a fair point to be made here about Fundamentalism in the US. Though I would point out that belief is certainly central to both Catholicism, Orthodoxy, and Mainline Protestants. When we look at Mainline Protestantism we can see different ways in which the Mainline churches engaged with modernity as compared with Fundamentalism. Where Fundamentalism challenged modernity in its own way here in the US, there was in the early 20th century something else that transpired in European theology, one of the most important being Swiss Reformed theologian Karl Barth. Barth's challenge to the prevailing Liberalism was not about a hoisting up the barricades and asserting rigid propositionalism (as Fundamentalism had done). Out of Barth and several others came what is known as Neo-Orthodoxy, and with Reinhold Niebuhr as a major Neo-Orthodox player on the American scene. So the Mainline tradition's engagement with modernity was less a fierce battle going on the offensive or defensive, but instead an engagement with modernity and the pursuit of Christian confession in the modern world. Modernity wasn't "the enemy" but a cultural force that needed to be engaged with, with Christians seeking how to engage their faith in the modern world. Liberalism and Neo-Orthodoxy have been significant forces in the Mainline Protestant churches, and the two are not exactly best friends, but the result of this has largely been a much more cordial relationship with the modern world, with forces of social progress, and the scientific community.
This has also meant more things:
1) Fundamentalists and the Neo-Evangelicals (more-so now than in the past I'd reckon) regard the Mainline traditions which had a more open engagement and cordial relationship with modern culture as abandoning or rejecting the faith. Creating an animosity that has resulted in denominational divisions, as well as vitriolic rhetoric from the particularly loud.
2) The Mainline churches, unlike the Fundamentalist/Neo-Evangelical churches haven't had the major influence of Pietism and Revivalism and thus have largely never been the sorts of churches from which you'll find people going to stand on street corners shouting at passers-by that they need to get saved. This means a couple other things, the Mainline hasn't invested in a sort of evangelistic activity that is largely antagonistic, both to other Christian traditions or to non-Christians more generally; you will therefore likely find fewer Mainliners who are in the business of telling other Christians they aren't really Christians or trying to make other Christians leave their church and join theirs with all the usual threats of hellfire, damnation, and salvific exclusivity (e.g. "you need to leave your dead church because you were baptized as an infant which really doesn't matter, you need a personal relationship with Jesus, and you need to be on fire and be telling everyone else about Jesus right now, do you really want to be responsible for your friends and family going to hell?")
American Mainliners are probably going to not be fundamentally much different than their European counterparts, while both are going to be quite different from American-style Evangelicalism and Fundamentalism.
It seems very often that Evangelical-style devotedness represents a more "serious" faith. I have on several occasions had people remark that I don't seem all that devout--which puzzles me. I consider myself very devout and take my faith very seriously. The real difference seems to be that my devotion doesn't look as flamboyant as, say, the Fundagelical crowd's. So what "looks" like fervent devotion to many outside the Church is most likely simply their observation of the way Fundamentalists and Evangelicals "do" devotion. At my church we don't see much reason to clap unless the children put on a production. Whereas applause is a fairly regular expression of devotion and faith during Evangelical styles of worship. It may therefore seem as though we're less enthusiastic or excited about worship, but that isn't the case at all.
These are all things that I think contribute to the current landscape of American Christianity.
There is a tendency to sound the alarm among some, there's this idea that Christianity is "dying" in Europe. As though there'll be a point in the near future when people won't be going to church or that people won't be Christian in Europe. To be perfectly honest I don't think that's realistic. Christianity may be shrinking, but not dying. I very much doubt that the churches in Europe will one day suddenly be completely empty. I do not come from a point of view that Christianity's strength is in its numbers. There was, at one point, a time when Christianity was nothing more than a little more than a dozen men and women hanging out in Jerusalem for about week. So the numbers game seems, to me, rather trivial. I think what we'll see is simply that the people who stay and keep the churches filled are the people who want to be there. Christian numbers may be shrinking in some places and in some ways, not Christian faithfulness though. I don't think that's going anywhere. I don't see Europe and think a place where faith is dying. It just looks different sometimes than what faith in America looks like; and the fact that many who grow up in the Church leave isn't new, that's always been something that's happened (though in times past there were, perhaps, social and political structures which may have hampered departure from the Church).
There's a parable that Jesus offers about seed sown, in some cases the seed begins to take root but is burned out by the hot sun, in some cases the seed is immediately plucked away by birds, in some cases the seed takes root and grows but is later choked out by thorns and weeds, and then there are cases where the seed takes root and grows and flourishes. Sometimes people grow up and then don't believe any longer, sometimes they just never believe, sometimes they believe for a time and then no longer believe. There are all sorts of scenarios that are out of anyone's hands, but then there there are people, and there always are people, who believe and will continue to believe. All such things are in God's hands, not anyone else's.
-CryptoLutheran