It's my opinion that the Outfit was the most powerful criminal organization in America under Capone, Accardo and Giancana. That would be the 20s and then the 50s-60s, diminishing steadily since.
To tell you the truth I don't know a lot about the East Coast mafia. I suppose we would have to decide on a metric of what "power" meant and then look for supporting data. From what I've read Capone's reign was singular and Acarrdo instituted a truly horrifying mechanism of corruption that essentially allowed the Outfit dominion over the city of Chicago, Vegas, Hollywood and all the traditional mob rackets west of the Mississippi. The level of corruption, the unions they controlled, was mind-boggling. The Chief of Detectives of the Chicago Police--not once, but twice!--turned out to be a mob shill here. Judges were straight out bought and paid for, up until the early 90s. A known and high ranking mob member controlled the most prominent ward in the city for decades.
Like I said, at Capone's height he had around 3,000 people working with/for him, and was, personally, worth a billion dollars in nonadjusted money.
Tommy Accardo and Sam Giancana expanded the Outfit's influence politically to a degree that would shame most Americans. Just how far it went will never be fully known but, as I mentioned, it's a fact--an embarrassing one--that the CIA did really approach him to help with the Castro assassination.
Maybe NY's Five Families tentacles reached just as far. In the limited reading I've done on them, I never encountered that.
