They implemented very harsh measures that are currently unthinkable in western countries.
I live in Czech Republic, and I read in the news that some 16.5k Czechs went on vacation to Northern Italy _after_ knowing about the risks. Now we're all in quarantine, with plenty of restrictions. Numbers of infections are still very low, but so is the number of tests that were done.
People just did not take Covid-19 seriously.
I don't live in Italy so for me it's hard to judge, but could the difference in efficacy maybe be explained by the discipline of the people?