A good horse should be able to neck rein in whatever bit you want them to, whether it's a snaffle, curb, or bitless. The purpose of the curb bit is not to gain more leverage or have stronger cues (though that is why many people use them). The purpose of a curb is to allow more subtle cues. A horse in a curb bit should be able to feel even the slightest flick of the reins and you shouldn't have to actually contact the mouth with the bit in order to stop them. Simply raising your hand and lessening the slack in the reins should be enough. A curb, by design, also encourages a horse to lower their head and break at the poll because it puts pressure on the bars, jaw, and poll. All that can be acheived with a snaffle but the more complex cues from a curb just make it easier.