Different outfits are unlockable for Cole with some having benefits and others just appearance.

Unlockable	How to unlock
Chicago Lighting	Enhances accuracy with the BAR, Thompson, and the shotgun	Awarded for linking your game/PSN account to Rockstar's "Social Club".
Golden Boy	No Bonus Awarded for reaching Traffic Desk.
Hawkshaw	Damage Resistance Awarded for reaching rank 18.
Sunset Strip	No Bonus Awarded for reaching rank 8.
Sword of Justice	No Bonus Awarded for reaching rank 3.
The Outsider	No Bonus Awarded for reaching rank 13.