Why did I choose the Gambinos? Because the Genovese's "don't break their capos, they kill them" as the Chin more or less put it. That means one mistake, and then whack! Then imagine what they do to soldiers.
I'm pretty sure they don't kill for any mistake.

Even so, how many Genovese captains have been murdered recently? I'm not keeping count, but the only one I can think of is Lawrence Ricci 9 years ago. But he didn't simply screw up, he disregarded a direct order.