I'd have to agree with everybody here on most points, but maybe question a few others.

Agreed the Irish had immigrated earlier than both the Italians and Jews, and had infiltrated both the underworld and because of their ability to speak the native language (English), quickly assimilated into politics and government. By the time the other ethnicities came along the Irish were solidly in control of government institutions which greatly helped their cause whether it be legal or illegal.

Even with the initial advent of those other two groups integrating themselves into the criminal world the Irish mobs were still very strong through Prohibition I'd say. But by the end of Prohibition (by the mid and late 1930s) the Italians had mostly seized power. The Jews had also more than come into their own by then as major powers.

From that point forward, the Irish underworld started to peter out a bit as they better assimilated into the mainstream of America. Not that there were not Irish gangs still around who operated successfully (like Eddie McGrath and Cockeyed Dunn and their Arsenal Mob), but their overall power had mostly given way to the Italians. Both groups only operated in certain sectors or the underworld economy; the Westside waterfront, certain labor unions, gambling, certain swaths of territory both in New York, Boston, Philadelphia, etc., whereas the Mafia was a mostly monolithic Octopus-like entity smothering nearly all sectors of the underworld.

And I see the Jewish Mob as working hand-in-glove with the Mafia as partners to better infiltrate both the underworld and upper world as they too morphed into business, unions, legalized gambling, etc.

Although the Mafia maintained much of the same interests, because of their massive national (and international) spider-like network of "borgatas" they maintained overall control of the nation from that point forward. All other entities, regardless of ethnicity or capability, essentially served as "junior partners" from that era forward. Cosa Nostra was just to big and well organized to buck.

But it's an interesting discussion and debate for sure. At one time in this country the Irish mobs were powerful; Jack (Legs) Diamond, the Dunn-McGrath Mob, Owney Madden, etc.