The single jointed or Cambridge bradoon works basically the same as its regular snaffle counterpart. The jointed action allows the rider to put pressure on one side of the mouth more than the other, and hence have better control over the lateral flexion of the horse.
However, with the single jointed snaffle, there is a certain amount of nutcracker action that can occur with greater pressure on the reins. This pinches the tongue, and on a horse with a low palate (or a high tongue) can also put pressure on the roof of the mouth, causing discomfort and possibly leading to resistance by opening the mouth.
Because this action is accentuated by thinner bits, it is possibly less desirable in a bradoon, which tends to be thinner than a regular snaffle. If it is a problem, using a shaped mouthpiece or a double jointed snaffle will usually alleviate the discomfort.