If inflation (or more precisely, the inflation forecast) rises above 2 percent, their strategy clearly dictates that monetary policy tighten. But if inflation falls below 2 percent, the ECB is not under the same pressure to ease – at least until inflation (or the forecast) threatens to fall below zero.
I believe the most important considerations behind the different monetary policies pursued by the FOMC and the ECB are due to differences in circumstances – differences in initial conditions and differences in the mix and intensities of supply and demand shocks.