My husband and I bought his first horse last year. She was a QH mare who had only been ridden western (we ride in english saddles, take lessons from an eventing trainer and foxhunt). When we tried her she was being ridden in a tom thumb type curb bit.
We switched her to a snaffle right away and had zero problems. But she's a naturally lazy sort, so "whoa" is not a problem not matter what bit (or not - she's equally easy to rate in a halter or hackamore) she's wearing. The one thing I've had to work with her on a bit (and am still working with) is to get her comfortable with being ridden with a bit more contact as that is something my husband had started to play with a bit in his lessons and not something she had had experience with before.