Bigger bits are used for refinement. That means that I can get my horse to do exactly what I want them to do in a halter, but when I have to move my hands 6 inches in a halter to achieve the same cue that I can get in a curb bit by moving my hand 1 or 2 inches. It's not about "use what works" because anything works. It's about "use what is the most subtle and gives the clearest cues". In a halter to do certain things, I have to apply a few ounces of pressure to the rein in order for the horse to understand exactly what I am asking. Compare that with being able to lift one rein by 2 inches, never contacting the bit to get the same reaction.
Think of it like this. You remember those can telephones that we all used to make as a child where you poke a hole in the bottom of a couple of tin cans and tie a string to them? Then you can talk to another person from one side of the room to the other? Remember how garbled and muted the voices were so that you could barely understand each other? That is the equivalent of a halter or soft bitless bridle.
Now think of how clear conversations are on your home phone, where you can barely whisper and the other person understands exactly what you are saying. That is the equivalent to a curb bit.
Yes, both of them work, but for finer cues and clearer communication, a curb bit is the best. Of course, that all depends on the bit being in the hands of a good rider.