Okay time to weigh in! I adore Full Moon Brotherhood, i have been trying to play shooty fourth ring, with mixed success, since i started playing the game and FMB massively enhances this archetype.
Firstly turning of a trait. Some times, as @Harlath mentioned, you only get to turn off a Irving, which i would argue is still not bad, but at other points turning off a trait is huge. In one game at the Euro Championships it was keeping a 4 stud out of shoot outs by turning off Nicholas Krammer. It also turns of Smiley, which can be game winning, and the likes of Tommy Harden, which as i like to cheat a fair amount is huge.
Secondly the inability to move by card effects. Not as big as the trait removal but i have used it to stop a many bullet dude stakes just rose-ing into a shootout which proved very useful. Also stops tricks like make the smart choice.
Thirdly the inability to refuse call outs. This I never found to be that big, generally if i hit someone with it my opponent didn't want fighting they just sent them home before the call out, can see it being very useful in some situations though.
Finally the two ghost rock or two cards. I find this rarely comes up unless used alongside a kidnapping or other attack job as usually the person i want to turn the traits off of is not the one who goes in a shootout unless its down to the wire anyway. Is a nice little kicker when it happens though.
Just my thoughts