Vibration is translated directly from the ring to the mouthpiece in a true loose ring and you can also move the bit in the horse's mouth a great deal.
A full cheek with a small ring like a fulmer is traditionally adjusted a little higher in the mouth - not only do you lose the direct translation of movement from the ring to the mouthpiece, you also lose the ability to move the bit in the horse's mouth in the same way you do a loose ring.
So I fail to see the advantage, though maybe there's something I'd not getting - if I want the vibration/movement, I'd ride in a true loose ring, if I want the indirect lateral pressure, I'd ride in a full cheek. The fulmer seems to give a bad hybrid worst of both worlds.
(Wallaby, if the bit works for you, go for it. I'm here for the bitting theory conversation.)