I've seen both sides of the pond and would dare to say that Europe is currently doing substantially better than its overseas friend. But it's not competitiveness that will propel us forwards; it's cooperation that will help us stay ahead of the up-and-coming billion plus people behemoths in the east. Were it not for religious incompatibility (countryside US is far too conservative to my liking), I would even propone the idea of a north-atlantic superstate to be able to stay ahead of the game.
What happens in Europe affects the US and vice versa. Microsoft will tell you all about that. As will any European aviator.