The classic Law Dogs outfit gives you 1 extra GR compared to other starter outfits which is crucial given how comparatively expensive Law dogs dudes tend to be. It's ability however lets you do something no other outfit can, straight up generate bounty on any dude of your choosing if you have enough influence. This opens up a whole new dimension of play no other faction has the same access to!
Combos well with:
Bounty Hunter - This card basically defines this outfit as it is the only one it can be used consistently with.
Bad Company - Turns mediocre shooters like Travis into a bowel loosening 5-stud shooter. Just don't lose him or the opponent is going to get a massive payday!
Outlaw Mask - Generate 1 influence for you a turn if you keep the wearer stationed in town square! Wear four at once to quadruple your influence gain and combine with ..It's who you know for an absurd amount of stud bonus. All in town square of course!
B&B Attorneys - Doubles the bounty accumulation rate on a wanted dude!