I have to disagree.

If by greatest Italian American mobster you mean both the most significant and the strongest, I gotta go with Salvatore Lucania. In second place is Meyer Lansky, but he wasn't Italian, so that skips us down to the number three most important and powerful mobster, which would make him the 2nd most powerful and significant Italian American mafioso and that is none other than Frank Costello himself.

Lucania was the change agent without which there would have been no Commission. After that he demonstrates that he is head and shoulders in influence above any other living mafiosi by springing himself from prison(!). Then from his base of operations in Italy he helps forge the link between the Sicilian Mafia, the Union Corse, and the American Cosa Nostra, not to mention the OSS. He actually transcended the mafia. He was more than mafia.

Meyer. Without Meyer, there would be no Luciano. It was his and Lucky's brain power added together that made him and Lucky twice as smart as everyone else, cause two heads are often smarter than one. Meyer was also Lucky's muscle, the power behind the throne. Without Meyer, you don't have the successful elimination of Masseria and Maranzano to be replaced by the Commission. You don't have the reformation and modernization of the mafia. So Meyer was of the utmost significance as a boss and he was as untouchable as Luciano himself which meant he was powerful. Forget about it.

Frank Costello was the connecting link between the upper world and the Underworld. Frank gave the mob all the power it needed that a gun could not give, which was the majority of it's power. And whoever heard of a non violent Godfather of a mafia family? You have to be mighty powerful to not even need a gun or demonstrate violent tendencies. In Luciano's parlance, "you gotta be pretty tough".

Real power is not needing to use it. And that's what Frank was.