I find that there are two types of oral & maxillofacial surgeons in terms of qualifications.
Either they are predominately dentally trained and registered, or, they are predominantly medically trained and registered.
I only work with medically trained oral & maxillofacial surgeons, as they have a wide training base, and are most able and trained in all facets of surgery. "Dental" Oral & Maxillofacial surgeons tend to be very limited in the scope of their work & have a poor wider understanding of medical, radiological and generally of wider surgical care.
I know the dentists say they were trained in medicine as part of their surgery training... But so are hospital nurses. No medical doctor or medical oral & maxillas facial surgeon would claim equivalence with anti e who's basic training is in dentistry alone.
However, I also look for Oral & Maxillofacial Surgeons who have a wide and demonstrable experience of orthognathic (jaw correction) surgery. I look for expertise in basic operations, as well as experience in a wide range of operations... Just so I know that not all patients are offered one operation type because that is the limit of their training or experience.
What I mean to say is that there are many kinds of operations, and real expertise comes with knowing all of them, and maybe even using them all for treating one condition.
For instance a person might have a chin point 3cm short of ideal. A BSSO can only safely advance to 10mm, but some try 12 or 15mm only to have it "come back". A better surgeon would offer jaw distraction, of say 15mm, then later a BSSO advancement (whilst also advancing the upper jaw) of 10mm, then offer a genioplasty (chin) advancement of a stable 5 or so millimeters. That means the patient achieves an ideal overall distance of lower facial advancement, gets a perfect bite, gets a maximally open airway (so they never snore), and they have an ideal jaw line.
These surgeons are rare though.
You should always look for examples of their work... And don't accept cartoons, or maybe case presentations from books to explain process. Look for real proof that the surgeon is capable of excellent results, by using examples of their own real patients.
Remember that surgery is also an art. You wouldn't expect just any painter to have the eye of DaVinci.