I think it is widely accepted that Paul "the Waiter" Ricca was the boss, with Tony Accardo as second in command. Giancana was appointed to run things on a day to day basis after Accardo got indicted for tax evasion, but all major decisions went through Ricca and Accardo.

After Ricca died, Accardo was the undisputed leader of the Chicago Outfit. Giancana and Accardo had a falling out over Giancana's highly publicized "lifesytle".

Best way to catch the smart ones? Get an idiot working for them.