Actually no, they don't. Especially the continental universitites. Well, I won't say they don't hold a candle, but they are usually ranked below the US ones in general. Even if we said they were equal you can't rank a nations university system on two schools. The real damning problem for Europe is that of the top 100 universities in the world, more than half are in the US.
For reference, top ten:
1 Harvard University Cambridge United States (Massachusetts)
2 University of California, Berkeley Berkeley United States (California)
3 Stanford University Stanford, CA United States (California)
4 Massachusetts Institute of Technology Cambridge United States (Massachusetts)
5 Cambridge University Cambridge United Kingdom (England)
6 California Institute of Technology Pasadena United States (California)
7 Princeton University Princeton United States (New Jersey)
8 Columbia University New York City United States (New York)
9 University of Chicago Chicago United States (Illinois)
10 Oxford University Oxford United Kingdom (England)
http://en.wikipedia.org/wiki/Academic_Ranking_of_World_Universities,_2010
Thats good for the UK being such a small country, but still not enough to claim a better university quality than the US. The UK unquestionably destroys the rest of Europe though, which is very odd. Why do continental universities systems trail so badly?