The Williams cheek piece allows for multiple rein positions. If connected to the main ring the bit acts as a loose ring, but when connected to the bottom ring it promotes pole flexion by creating more positive poll pressure. The Williams cheek piece helps to prevent drifting.
The Mullen is a strong bit which creates direct pressure on the tongue. Used for a strong older horse and will also bring the head down.
The material used allows the bit to remain light and it encourages salivation. It is particularly well suited to horses that object to metal mouth pieces.