DC, I'd have to say, "none of the above":

Bugsy Siegal--Got his "bug" rep as a kid. As an adult, mostly a (ruthless) businessman.
Vinny " Mad Dog " Coll--that name was given him by the newspapers after one of his attempted hits went bad and he killed a little kid with a stray shot. Otherwise, he was a fairly conventional thug-for-hire.
John Dillinger--your basic bank robber, made into a popular hero (ironically) by the FBI's efforts to aggrandize themselves. He was a font of sanity compared with his sometimes gangmate, Baby Face Nelson, who was a real nut-case.
Al Capone--his only real "craziness" was caused by his tertiary syphillis. Committed two murders as a teenager, one as an adult. That's all.
Joe Gallo--he created the "crazy" name for himself to make up for the fact that he was small of stature and needed a "rep" to enforce his will as a small time racketeer.
Sammy Gravano--definitely a methodical killer, but always in the cause of business or personal advancement, usually when someone told him to kill. Something like a Nazi war criminal: "I vas unnnly obeying orders."

IMO, the crazy Dons were Albert Anastasia and Carmine Galante. Anastasia committed more than 50 murders by his own hand. As Don, he ordered the murder of Brooklynite Arnold Schuster simply because he gave the cops a tip that led to the arrest of Willie (the Actor) Sutton, a bank robber and prison escapee who had no connection to the Mob. To me that's crazy. Galante was a stone killer and sadist who ran the Federal lockup in Lewisburg, PA, like Nero ran Rome, and whose cruelty was legendary.