I can tell you that, having seen some before, injured, and transplanted photos of facial transplant patients, their faces rapidly look much like they used to, regardless of the original person their face was transplanted from.
Bone structure is, as far as I can tell as a layperson, the major determinant of how people look. I found it quite surprising as I thought it would be the other way around.
The only obvious change was hair and skin color, essentially.