I use a mullen mouth because I start with "simple" and move to "more complex" if needed. I usually know within the first couple of lessons whether or not that is going to work, and then will move to a French Link or something else. I rarely use a single jointed snaffle anymore.
At both the Larry Poulin clinic and the Suzy Stafford clinic, they gave the impression that a lot of drivers (at least in the Midwest) over bit their horses, and then don't use enough rein contact. Both clinicians changed out a lot of bits, mostly jointed ones to bar bits, either arched or ported. Larry really likes the Glory bits. Suzy brought her stash of favorite bits, and not a one was jointed. One gelding that Larry worked with was like a different horse when he was finished dumping the common single jointed snaffle for a Glory bit.
We normally use a sloted Uxeter (low port) Kimberwicke on Spider (our big horse) in the lower setting, but Suzy said that was too much for him. However, when I said that he gets pretty ambitious at the pleasure shows, she said that we might have to use the lower slot when he has "competition" in the ring, but the upper slot for dressage when he is in the ring by himself. She was very happy with his performance with the rein in the upper setting.
The key is to keep the options open and not be afraid to try what works, with a bit of "educated guess" thrown in. What was really cool was to hear Larry say over and over, "Watch, this horse will do X," and by golly they would!
Myrna