A horse shaking its head when bit pressure is applied or its tongue trying to escape the bit are classic signs the horse has a sensitive tongue. With this in mind the Happy Tongue was created, it has a medium port creating space for the tongue, relieving pressure, allowing the horse to relax.
The Big Ring Gag is stronger than the usual Loose Ring and Eggbutt as the ropes going through the rings create leverage which will exert more pressure through the mouthpiece whilst at the same time introducing more poll pressure. These are generally used for Polo.
The big ring creates more leverage making it stronger than the small ring version.