This is education, not advice
The information here is written for the general reader and does not replace a personal medical consultation. It cannot tell you whether either operation is appropriate for your jaw, your bite, your health or your circumstances.
No outcome is guaranteed
No treatment can be guaranteed. Both operations work near the nerve that supplies sensation to the lower lip and chin, and that sensation can be affected; a bite relationship can relapse; a contoured jaw can be asymmetric or need revision; and either operation can be followed by a further one.
Contouring does not correct a bite
Cosmetic jaw contouring reshapes the jaw angle. It does not move the jaw or change how the teeth meet, and a bite that does not meet correctly is assessed and treated as a functional problem with an orthodontist involved.
Neither operation changes the teeth
Orthognathic surgery moves the jaws and the teeth move with them, which is why orthodontic treatment is part of the plan. Contouring does not move the jaws at all. Neither operation straightens teeth or replaces orthodontic treatment.