I think it's just the fact that both groups immigrated to the US and were thrust into the ghettos at the same time (displacing the Irish in the same way they displaced Daniel Day-Lewis). Both groups gentrified out as well in time, but the nature of "amici nostra" meant that the Italians, by initiating their younger family members and neighborhood wannabes, were able to maintain an effective hegemony over organized crime in some cities.

Lansky himself is a key example; even though he was certainly influential among earlier Mafia leaders, he never exercised any real power. He didn't collect tribute from the Italians, he didn't conduct sit-downs, and he certainly didn't order hits. He was strictly a "partner" to Joey Adonis and later Jimmy Alo. Granted, they were very easy-going partnerships, as he made both men extremely rich.