Requirements of a superpower according to political scientist W.T.R Fox (the person who created the "superpower" term):

Military Power
Nuclear Weapons
Diplomatic Influence
Economic Strength
Influential Economic, Social and Welfare Systems
Global Influence and Interests

Now, let's compare the USA and your two suggested rivals, China and the EU.

Military Power:

USA - Most advanced military in the world, with roughly 1.5 million active personnel (2006), military technology is world-class, brilliant deployment strategies (forces already stationed all across the globe), plenty of experience with asymmetrical warfare. In 2006, the Navy had 72 submarines, and 118 battleships, the air-force had 1,700 combat aircraft (with stealth craft - of which no other air-force currently has access to - I believe Russia has developed a craft, but it isn't currently deployed amongst air-force).

China - Largest military force in the world (roughly 2.25 million active personnel). Navy has 58 subs and 71 combat ships (again, 2006 data). Low deployment - relatively few Chinese forces stationed outside of China. Little/no experience in asymmetrical warfare. Has a larger air-force than USA, with 2,600 aircraft, but no stealth craft - all craft is typically of a lower standard than American aircraft (same could be said for navy). Military technology typically a generation behind the USA, and with nothing like FCS in the works, that gap could be growing, rather than shrinking.

EU - Has no real military force outside of the EU's rapid reaction battlegroups. This consists of only 1,500 troops. And it hasn't been deployed yet. As the EU doesn't have a co-ordinated foreign policy, only a common one, the RRF can only be deployed in areas in which all member states agree. The EU's individual members all have their own militias, of varying strengths and capabilities - however, in Afghanistan and Iraq, even the most powerful European militias (UK, France, Germany) have proven to be reliant on the USA for air-support, intel, etc. European defence, as a whole, is usually the interest of NATO - which includes the USA, not really much use for rivalling the USA.

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Nuclear Weapons:

USA - Second largest nuclear stockpile in the world, with the most advanced means of delivering them. The USA also has various projects in the works to block any incoming nuclear missiles, giving them an absolute edge in nuclear warfare.

China - Has nuclear weapons, and missile technology - but, again, the systems are technologically behind those of the USA. All very secretive, but it's assumed that their stockpile is small compared to the USA's.

EU - Worse than military, no fledging projects, two members have nuclear weapons - UK and France - but it is nigh on impossible for them to ever be used in the name of the EU - especially as both states (and USA/China) are members of the NPT, and handing the power of the nuclear arms over to an EU institution would b a violation of the NPT.

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Diplomatic Influence:

USA -  Leading member of United Nations (permanent member of the Security Council), NATO, World Bank, International Monetary Fund, G8, G20, World Trade Organisation. Extremely powerful regional influence, many strong bi-lateral ties with UK, France, Israel, Japan, Germany, Poland, etc.

China - China is also a major player in the UN, with a permanent seat and veto power in the Security Council, important player in the World Trade Organisation, has very strong regional influence, but it is crippled by a very powerful Japan next door which also has strong regional influence.

EU -  Didn't even have a foreign minister until the start of this year, and she can only have a say over areas where all 27 EU members agree. Of course, in the situations where there is unity over foreign policy (typically in affairs to do with Russia, the Balkans, Africa, the environment, and extreme weather disasters - such as Haiti), the EU does have a lot of clout. The EU isn't represented in most international organisations, the exceptions really being the World Trade Organisation, and the G20. The most important institution: the UN Security Council, there is no European representation - there's British and French representation, but they often differ on key areas (Iraq, most notably). Whilst Britain did declare its willingness to relinquish its veto power to allow for European representation (under Blair), France refuses, and, now, it seems unlikely that even Britain will support this notion under the new administration.

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Economic Strength:

USA - World's largest economy, largest trader. United States consumerism is the engine of the global economy, when the US stops buying, the rest of the world falls. Majority of the world's biggest multinational corporations are American, biggest names of globalisation are all American (Coca-Cola, McDonald's, Dell, PepsiCo, Nike, etc).

China - Poised to become the second largest economy at some point this year, China is now the world's largest exporter. However, China's economic growth is far less sustainable than Americas (in terms of resources consumed per dollar generated), has huge poverty issues, and a very low average wage. China's economy being dependant on exports means that, contrary to popular belief, China needs the USA more than the USA needs China. Lot's of talk about China's economy overheating, and its domestic economy isn't developing as fast as hoped (pretty much all investment goes into the export economy). Policies such as the one-child policy will harm China's future economic prosperity.

EU - Whilst the EU, as a whole, does have a larger economy than the United States, this won't last forever. The EU's only hope of maintaining a larger economy comes from adding new members: EU growth is lower than the United States, labour productivity levels are falling, and the population is ageing at a faster rate. The economy is the EU's strongest point, but even that doesn't hold a candle. It must also be noted that much of EU trade is intra-EU, so whilst Germany may be the second largest exporter, most of this stays within the EU.

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Influential Economic, Social and Welfare Systems

USA -  Democracy, capitalism, globalisation. Does much more really need to be said than this?

 China - China's "way of developing" has proven to be largely successful and many other developing nations, such as India, have started to copy their model. Chinese culture also plays a role in a lot of people's lives - particularly martial arts and cuisine, nothing compared to what Hollywood pushes out, though.

EU - The African Union's main inspiration came from the EU, also, it has resulted in the likes of the North American Free Trade Area (NAFTA), and other regional organisations. Culture is definitely out there: Italian and French food, British sports, that kind of thing. However, lot's of European culture is now heavily Americanized (more so than the other way around).

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Global Influence and Interests

USA - The USA really does have its finger in every pie. In just about every single international affair, America has some say, and, depending on the nations involved, a lot of influence (though dated, think of the Suez crisis as an example of America saying "jump").

China - One of the few countries that has any kind of influence over North Korea (perhaps the only country). Also, China has strong ties with countries like Sudan, which the West (USA/EU) have no control over. China has a lot of control in Africa, and a lot of regional power. China is also seen as the country which leads the poor in the World Trade Organisation. China's power is often exaggerated, though, with the USA ignoring its stance on most issues.

EU - Sometimes seen as the alternative to the USA for countries wanting to deal with the West. The EU has incredibly strong regional power (as most surrounding countries want in), the EU is also seen as a leader in the fight for climate change and foreign aid.

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Going by all this, I'd say something is very clear: the USA is the sole superpower, even hyperpower. The EU is far from it, and, probably never will be. China is also at a distance, but, unlike the USA, China has a reasonable chance of developing into a superpower, but it's still not guaranteed. It will probably be a couple of decades yet, before we really know how it's trending (during the 70s and 80s, people were talking about Japan becoming a superpower, and nobody knew what was going to happen to the USSR, for example).