There are about 850 billion euros and about 1.1 trillion dollar in circulation. However, after 2010 it appears that USD currency started to increase, while Euros after 2012 have plateaued and are now declining.
You can see this phenomenon more clearly if you look at the ratio charts; ratio of euros to total currency, as well as the ratio of the VALUE of euros over the value of total currency. The total NUMBER of euros as a percentage of euros + dollars peaked in 2010 at about 47%. The total VALUE of euros as a percentage of euros + dollars peaked in 2009 at about 57%.
What does this mean, and why do we care? I'm using this ratio as a proxy of "faith in the eurozone" - I also think it measures what the underground economy thinks about both currencies.