Began writing this five months ago somewhere between visiting Croatia and Slovenia. Tweaked it a few times since. It probably isn't going to get any better, so I am giving up, posting it, and walking away! :-D
Europe, a continent the size of the United States, boasts myriad languages, faiths, and cultures. Some countries there were fighting wars with one another as recently as the 1990s, and other forms of cultural wars continue to divide Europeans today. Thus, it would be silly to generalize about Europeans as a whole. But I'm silly, so let's do it!
Europeans seem to be more pragmatic and susceptible to logic than Americans, perhaps to a fault, as pragmatism sometimes leads to pessimism, and pessimism leads to inaction ("The odds are I will fail, so I will not attempt"). But I can relate better to this form of logic than to American optimism, and the longer this economy drags the more American realists I think there will be.
Europe contends with a Babel effect; even with English as a fallback business language there is a large, disenfranchised portion of the population that cannot so easily participate in the international market. America is fortunate in that its citizens by and large speak the same language.
The Muslim issue seems to be roiling Europe, whereas America's analogous Mexican immigrant issue is not so big a deal (the U.S. immigration debate does not represent an all-out "culture war" on a par with Europe's Muslim one; and regarding our own recent Muslim issue, the "Ground Zero" "Mosque" [both terms need to be scare-quoted], this appears to be a trifle compared to the all-out European cultural battle).
Europe has a deserved reputation for paying more attention to detail, and generally is known to produce a higher quality of product (from clothes to furniture to cars to women*) than Americans, though sometimes at unreasonable cost.
Even if we are to trust the gloomy international standardized test scores, the United States' 300 million-strong population guarantees that a large number of smart and clever people will continue to drive the markets and innovation. Lack of hyper-pragmatism means greater ingenuity and innovation--the best entrepreneurs expect to fail sometimes and are not easily dissuaded by failure. That means we sometimes fail epically, but we also enjoy epic success (McDonald's, Microsoft, etc.).
All that said, I often think I would rather live in Europe. I identify more with its culture and lifestyle. America can become great, but if my life isn't, then why stick around cheerleading the richest 1%? There are plenty of European democracies I could choose to live in. And did I mention the girls?