The Full Cheek will have the same effect as the traditional Eggbutt in so much as, it will prevent pinching on the sides of the mouth, however, the extended pins above and below the bit, firstly prevent the bit from being pulled through the mouth and secondly have the effect of guiding the horses head which is great for schooling and training purposes.
The Happy Tongue is a solid mouthpiece. It is curved and ported to give tongue relief. The Happy Tongue would be a good place to start if your horse is:
Shaking its head
Sticking its tongue out
Sucking its tongue back and as a result, making an intermittent coughing noise
Trying to put its tongue over the bit
Going behind the bit to avoid the contact
Snatching the reins forward and down
The rider will know immediately if this is the correct bit, as a horse with a sensitive tongue will finally begin to work into and accept the contact. Changing the cheekpieces would then allow the rider to adjust the level of control.