I ride T in an english hackamore. I ride with a lose rein and use my legs and seat mostly resorting to rein in speed control only as a reinforcement if she disregards seat. I neck rein and direct rein with no problems. She is light and obediant and a very happy girl.
Walka is ridden in a full check snaffle and is also light and responsive. He seems very comfortable with that selection.
I purchased a Dr Cook Bitless Bridle for T a few years ago, and she absolutely hated it. So, your horse will let you know if he/she is comfortable or not.