The only benefit I've seen to the Obedient trait is, you get more experience from co-operqting with Junius and Bibius (Obedient) than you do from killing them (Independent).
You can cancel that out in conversation if you join the Fantastic Five. I don't remember where the next Obedient/Independent check is, but as soon as you hit it, Bob's your Uncle (but you no longer give a damn).
All of that is irrelevant if you're role-playing your way through, in which case you'll do whatever your characterization demands regardless of the meta-game.
