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.
Our Snaffle is a popular bit due to the curved mouthpiece which distributes pressure more evenly over tongue and bars. With the offset centre link it will reduce nutcraker action and pressure points on the tongue.
The Square Twist will create more pressure points on the mouthpiece which will make it stronger than the Round Twist and Smooth.