Many Keynesian Monetarists would likely argue that a primary reason that the US economy is faring better than Europe's is that the ECB stayed tighter for longer than the Fed. Empirically, it's tough to argue with such thinking. Now that the ECB has undergone two separate LTRO operations though, the ECB's balance sheet has quickly caught back up to the size of the Fed's.
For now the expansion has had a limited effect on the European economy, but it may have had a greater effect on the currency than most are noticing. The increase in the size of the ECB's balance sheet may be an alternative explanation for the recent struggles of the Euro vs. the Dollar. The chart below compares the relative size of the Fed's balance sheet and the ECB's. It shows that since 2009 major trading patterns in the Euro have tracked the relative expansion of the ECB's balance sheet relative to the US. In times that the Fed's balance sheet expanded faster than the ECB's (the red line moves higher) The Euro strengthened relative to the dollar. In the past five months the ECB's balance sheet has grown much faster than the Fed's and the Euro has weakened. Of course, prior to 2009 this relationship moved in the opposite direction, but prior to then the monetary environment was a little more stable than it is today.