The "Despite Obama" Recovery
Why then is the American economy stronger than the European? Keynesians of course blame the weak European performance on "austerity", but the U.S. has in fact implemented austrity too in the form of both tax increases and spending cuts (the so-called "sequester").
Instead it is because of two things. One is that the U.S. economy is despite Obama still relatively flexible and free. This factor is illustrated by the fact that relatively flexible European economies like the Baltic countries and Ireland have performed best recently.
Another factor is the massive increase in production of oil and natural gas in America (with daily oil production increasing by 1 million per year!) . This isn't strenghtening the economy just because of the incomes that workers and capitalists in the sector receive from it, but also because it lowers the cost of energy. The latter means not only higher real wages for workers outside of the sector, but also strengthen the competitiveness of U.S. manufacturers and other businesses that use a lot of electricity.
The irony is that both of these factors are things that Obama oppose. Obama wants to make the economy less flexible by for example raising taxes and the minimum wage, and Obama is also negative towards oil in particular because of all the carbon dioxide emissions it creates. And indeed, by for example stopping the Keystone pipeline, Obama has made the oil boom smaller than it could have been.
So this is certainly not an "Obama recovery", more like a "despite Obama recovery" or "Recovery due to things Obama oppose".