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.
The Ported Barrel was created to relieve pressure on the tongue via the the medium port, which creates space for the tongue. The Barrel joint relieves pressure on the bars by spreading it over a larger area and limiting the nut cracker action of a conventional snaffle.