The Euro is outcompeting the dollar bedcause the dollar is in the midst of a serious inflation that began in the Fall of 2000. When the US trashes its currency by pushing too much liquidity into the system that currency falls in value relative to another currency whose government is not engaging so heavily in inflation. The Euro is not "improving" due to any inherent trait of its own. Its producing government has not yet grabbed the tiger's tail.
All things being equal, the Dollar is still losing ground against the Euro.