Here's a different answer. Usually I endorse bitless, because that's how I ride. However, I am going to be using a snaffle bit, and eventually a curb bit, to rein with.
So to your question in the OP- Both.
Work towards being able to control your horse in a rope halter one day, and a bit the next.
Bitless riding and training is different. You cannot expect your horse to just "take" to it. You must work on the ground, lunge, and let your horse learn what is expected of him bitlessly.
It is my opinion, that ANY well-trained horse, unruined by abuse, hard hands or excessive force, with enough time, effort, and knowledge, can be successfully ridden both ways.
If a horse is "uncontrollable" bitlessly, it is not the headgear's fault. It is a rider/training/discomfort problem.