An "exclusive mode" using a "signature weapon" was announced for the PS3 version of Saints Row: The Third at E3, but it doesn't appear to be in the final version of the game.
Volition and THQ had yet to decide on the final extra content at the time, and according to Joystiq, who has rigorously compared Xbox 360 and PS3 copies, it never actually eventuated.
THQ responded to questioning with a standard "no comment".
Of course, it could be coming through DLC or a later update. It's also speculated that the wave-based "Whored Mode" could be the "exclusive", but THQ wouldn't confirm or deny anything.