I suppose you mean public (government) debt?
The 27 countries in EU had a total public debt of 10.8 trillion USD in 2007, 58% of GDP. (Debt in Euro for 2007, converted to USD at today's exchange rate.)
For comparison, USA had public debt of 11.2 trillion USD in June 2009, 81% of GDP.
Public debt in Europe has presumably increased since 2007, as European governments have dealt with the financial crisis with public spending much like USA has. So the numbers given here aren't really comparable (Europe pre-crisis and USA post-crisis), but I couldn't find more recent data for Europe.
Although as a first approximation, the level of public debt seems to be similar.
See related links, including the list of countries by public debt (2008 data).