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 conventional Snaffle joint has a nut cracker action, which means it will bear pressure on the horse's bars and the tongue. The Barrel joint limits the nut cracker action and spreads the usual pressure over a larger area. When the rein is used this mouthpiece wraps across the tongue creating tongue pressure and taking pressure off the bars due to the lock up action. Please note appearances may be deceiving, this bit joint is stronger than the Elliptical as pressure is more concentrated on the tongue as this joint is smaller.