Actually it makes a HUGE difference and this is a very, very good question.
I had an Asian (Chinese) jaw surgeon during my first consults and he indicated that a lot of the traits I wanted to achieve (very strong chin, long jawline, high cheekbones etc..) well they were particular masculine ideals more prized within a white-aryan looking context and that in other cultures such features weren't so heavily regarded as beautiful or masculine or prized.
It's funny cause this raises issues about whether beauty is crosscultural and cross-racial ideals are the same or if it is different in different cultures --which it most certainly is if we just look at the evidence historically.
So this CHinese surgeon, while he was open to taking me in the cosmetic direction I wanted he also made me aware of some of the racial and cultural implications of what I was doing.
I mean it's racially true that people from my part of the world have thicker skin, some have thus larger more bulbous noses. Blacks have usually more protrusive maxilla and some have less prominent lower chins even though their jaw structure is fine. Should they be "normalized" to some eurocentric ideal? I would say no, that sounds like butchery not surgery to me.
It's a complicated issue. Most important thing is to have clear communication and set of expectations with your doctor. If that requires five f**king meetings where you ask him to repeat back or draw exactly what he or she is going to do and it mirrors what you wanted or you get an explanation of what IS possible or what they'll go for, well that's what's important. Don't assume they'll do anything regardless of their race.