It is good to remember that US and European policies in number of international issues were allready different during Clinton regime. For example US and european policies in human rights (vis a vis death penalty), international court system, international environmental policies were all very different. Similarly policies towards Israel's actions were also quite different.

The real reason why US-European relations appeared successful were that Clinton's skilled use of both internationalist and unilateral approaches to foreign policy. US did had its head most of the time but did not antagonize nor demonize its European allies. The rift became open because Bush has been rejecting this kind of diplomacy and replaced it with more unilateral policies (that were evident from his early days as president).

Socially US has also been moving different from Europe. There has been discussion of "New England's European Culture" being replaced with "Cowboy Culture of South" in US. Meanwhile the older generation whose memories are ruled by WW2 are being replaced with never generation looking more national (and nationalistic) cultures in Europe. While this is perhaps somewhat exaggeration the generational change of guard happening in 1990's to now is reality.

US historical perspective is shorter and more triumphant so belief one's perfection (and subsequently rightneousness) is stronger. Memories of failures were certainly fading (I noticed this reading US Army manuals where Vietnam was not mentioned as war US Army had been gaining experience at all!!). Triumphalism and national chauvinism were certainly rising allready in Clinton era but it was accepted in Europe as US behaved then acceptably (see above to methods used in Clinton regime's foreign policy).

Finally, there has been studies of early Bush II foreign policies and I personally found out that US was officially changing its strategic priorities from European centric strategy towards Pacific centered strategy (Rumsfield authorised series of reviews and parts of them were leaked to press). The goal then was to make China new opponent (as new USSR) but this was moved under carpet soon after spyplane incident. Then 9/11 happened and US policies were totally moved towards new Middle-East policies. Afganistan invasion was carried out practically unilaterally (despite offers from NATO countries to participate) and the breakup was total with Iraq where combination of bad foreign policies and mistakes led to breakup between France and US (there has been rumours that spite was due diplomatic errors but I quess I have to wait decade or two to learn the actual truth).

But that's not the whole story, since those reactionary tendencies are unfortunately in evidence elsewhere in the world, in Europe too. People feel threatened and insecure and batten back on to identity politics -- mostly national and religious chauvinism. What distinguishes the US, imho, is that you have a pretty huge stock of unregenerate heartland reactionaries who were just waiting for a little encouragement to come out and take front centre stage...