American Society of Plastic Surgeons (ASPS) or American College of Surgeons (FACS)?

There is only one board recognized by the American Medical Association for the training and certification of plastic surgeons.  That board is the American Board of Plastic Surgery.  Unfortunately, there are a number of doctors out there from other specialties who take weekend courses in cosmetic surgery and then call themselves "board certified (in something) plastic surgeons."  If your doctor is certified by ABPS, you will know that he has undergone the most rigorous training and certification requirements and is a legitimate plastic surgeon.  While this does not guarantee a result, it will give you your best chance for the best result possible.  ABPS certification is the most important of the three groups that you mentioned.

   If all three are certified by the American Board of Plastic Surgery, it probably does not matter about the other two.  The addition of ASPS, for example, involves filling out an application, getting 2 recommendations, and paying dues.  You are not eligible for ASPS until you are Board Certified by the American Board of Plastic Surgery.