I think Americans are exceptional, which doesn't need to mean "the best at everything."
1) Americans are, historically, exceptionally willing to let immigrants integrate. My family is from Bangladesh, my wife's from Oregon, both going back many generations. She could never integrate into Bengali society the way I have been allowed to integrate into American society. She could live there her whole life, and she'd always be "bideshi" (foreigner).
2) Americans are exceptionally optimistic. At its best, Silicon Valley is uniquely American: too naive to know that you can't do that. This is a double-edged sword, of course. Most of the time, "you can't/shouldn't do that" is true.
3) Americans have an exceptional commitment to the rule of law. We're not at a high point in our history in this regard, but we're still a society where the great struggles of our day play out in front of courts, not in riots and mobs.
Now, we're not as exceptional as we used to be. But in large part because Europe spent the last couple of decades becoming more like us. They instituted market reforms, opened up to immigration, rooted out corruption. It's easy to say that America isn't exceptional if you pretend European history didn't happen prior to 1995.