"Greatest" isn't a term I'd use to describe any gangster.

The most influential, IMO, was Charlie Luciano. He ended the regime of the Moustache Petes by arranging the assassinations of Joe the Boss Masseria and Salvatore Maranzano. He brought Cosa Nostra into the modern, business-oriented era by accepting help from non-Sicilians and even non-Italians. And, he formed the Commission, which introduced an element of cooperation among the families.