The Eggbutt cheekpiece prevents pinching of the lips and give a slightly more solid feel against the side of the face. It also prevents the bit being pulled through the mouth. The release is slower and also introduces some poll pressure.
A Ring cheekpiece introduces poll pressure as well creating leverage on the mouthpiece, the 2½ Ring version is the softest version of ring bit as the ½ ring softens the leverage on the mouthpiece and poll.
The Happy Tongue is a solid mouth piece. It is curved and ported to give tongue relief. The Happy Tongue would be a good place to start if your horse is:
Shaking its head
Sticking its tongue out
Sucking its tongue back and as a result making an intermittent coughing noise
Trying to put its tongue over the bit
Going behind the bit to avoid the contact
Snatching the reins forward and down
The rider will know immediately if this is the correct bit, as a horse with a sensitive tongue will finally begin to work into, and accept the contact. Changing the cheekpieces would then allow the rider to adjust the level of control
The Cherry Rollers roll in the horses mouth giving him something to play with and reducing the likelihood of the bit being held in the horse's teeth. They are constructed tightly so there is no chance of pinching. When pulling on the reins, the rollers allow the bit to move along the bars of the horse's jaws as opposed to rubbing.