The Eggbutt cheek piece 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 horse shaking its head when bit pressure is applied or its tongue trying to escape the bit are classic signs the horse has a sensitive tongue. With this in mind the McHardy was created, it has a medium port creating space for the tongue relieving pressure. The Buster Roller in the middle increases bar pressure and as a result lifting the horse's head and giving more control.