The EU as a direct counterpart to the US: That was the whole point of it, after all. The US is so 'big' and 'bad', and the whole world is so afraid of us, that Europe wanted to merge all their separate powers into one big superpower, just to be able to contend with us. I don't know whether to feel sorry for them or not. We're obviously the whole reason for the EU's existence. This obviously has bad ramifications for us, specific ramifications that we are unaware of at this time. It also has bad ramifications for them (being overrun by the Muslim hordes, for one). But the European nations were willing to give up their sovereignty in order to become a superpower, to be able to match our power. That's why nations are clamoring to get in to the EU. It's sad, for the individual nations' loss of power, and for the eventual Muslim takeover (that's the way I think it's headed). I feel more sorry for them, at this point, than I do for us. When the US and the EU start having clashes, then I'm sure that will change.
Nope. Being a political or military superpower is neither effective nor desirable for us Europeans. Why? It would require huge investments into defense if we should enable us to project power. You Americans have to spend billions and bazillions and last but not least thousands of American lives for maintaining your superpower status. Projecting power means lots of conflicts in areas far from our real interest zones. We Europeans can live with a defense that is suitable for our continental needs.
In economical regard the EU is already a superpower. The US has a GDP (purchasing power parity) of $13.06 trillion (2006 est.)and a real growth rate of 2.9% (2006 est.) while the European Union as a whole has a GDP of $13.08 trillion (2006 est.)and a real growth rate of 3.2% (2006 est.) (source: CIA-factbook). That means we already have a slightly bigger economy in Europe than in the US. Nevertheless much has to be done. We have i.e. great differences in per capita income among member states (from $7,000 to $69,000). Therefore you will feel our main efforts rather in our own backyard than in animosity with the US.
P.S.
This American blahblah about Eurabia is quite ridicolous from our side of the big pond. Most muslims in Europe are social underdogs with practically no education. They are simply far too dumb and for sure not enough to build up a "caliphate". 3.7% of the German population are Muslims from Turkey i.e.. If they should try they would loose their welfare check immediately. As far as I know you Americans have also your problems with your minorities. Maybe you remember the L.A. riots in 1992. The damage and the blood toll there was higher than the one in the recent riots in Paris i.e..