A double-jointed snaffle is actually milder than a single-jointed snaffle. The pressure is distributed to more areas of the mouth and dispersed.
The hanging-cheek aka baucher bit you are looking at would actually be milder than a single-jointed snaffle. Despite its appearances, the hanging cheek works no differently than a regular snaffle.
There is no leverage on the bit so it basically works the same as a simple snaffle. It is possible that there is a very slight amount of pressure on the poll, but not enough to affect the horse.
The Kimberwicke, on the other hand, would be a small step up from a simple snaffle. It has slight leverage, and is like using a curb bit with a very short shank. Because the shank is so short, it does not have the difficulty of instability in the mouth and mixed signals to the horse that other jointed shanked bits can have.
Which brings me to the other bit with the shanks. With a curb strap on this type of bit, there is a lot of leverage so it cannot be ridden in with constant contact (best used with neck reining). Without a curb strap, the bit will rotate around uselessly, pulling the bridle out of place and sending unclear signals to different areas of the mouth.
A good reason to use a Kimberwicke is on a horse that is well-behaved and can be ridden lightly most of the time but on occasion needs the stronger signal of a mild curb to get the horse's attention.