What is the difference between monkfish medallions and monkfish cheeks? Location. The tail, where the medallions are processed, delivers that signature firm, meaty bite and mild, lobster-like flavor that holds up beautifully on the grill. It’s versatile, hearty, and made for bold cooking. The cheeks, on the other hand, are a true hidden gem and processed from the head of the monkfish. Smaller, more tender, and naturally sweeter, they offer a delicate, almost buttery texture