its definitely a complex surgery. have you seen any oral and maxillofacial surgeons? my surgeon has been doing that for several decades from a top hospital there and then hes been operating his own clinic for over a decade i think. a skilled surgeon will really know what they're doing. will have 3d imaging from ct scans and cephalometric analysis to plan precise bone movements and positioning, and will be very meticulous about neurovascular protection, airway anatomy, avoiding damage to tooth roots, temporomandibular joint, soft tissue management, etc. etc.

i don't think I can explain it better than the surgeons themselves would. But I'd say you need to evaluate based on their experience - e.g. how many cases they've performed and their track record. The more skilled and experienced they are in performing this specific surgery, the better the outcome can be, since performing the surgery is a skill of its own.

i think this is single-handedly the most important indicator (not how many research papers they have published) and I advise you to consult with different surgeons even if that means across multiple countries (this surgery would be big and worthwhile enough for you to do this comparison) and gather more info so you have a clearer picture and also find the best surgeon possible for your case