I am a Facial Plastic Surgeon and proud to be so. Obviously, my perspective is biased based on my training, a training devoted to the face and neck.
However, I think there are several observations a prospective patient should consider in making their decision.
The Individual Surgeon:
I can assure you that if you are seeing a Facial Plastic Surgeon or General Plastic Surgeon, there is a high probability you are seeing a surgeon who has excelled academically and clinically in Medical School, Residency, and post-residency training. Both specialties have a very high percentage of Alpha Omega Alpha graduates, and both specialties are highly sought after as residencies, and therefore highly competitive. These attributes definitely don't assure good technical skill or an artistic/aesthetic sensibility, but they are a good start.
Both Facial Plastic Surgery, and General Plastic Surgery have legitimate claims, as specialties, to providing expertise toward cosmetic and reconstructive procedures of the face. As other posters have correctly stated, the individual surgeon may have been in a residency program where there was minimal or major emphasis on facial anatomy, surgery, or pathology. Learning technical and judgmental skills in surgery is not a one step process; it requires careful study and consideration and an ability to apply a three dimensional approach, understanding that every action has an equal and opposite reaction. The failed Rhinoplasties/Facelifts of countless Hollywood celebrities provide proof that these concepts can be difficult to learn. Facial Plastic Surgeons obtain training in cosmetic surgery both in their residency training and in their fellowship training; this training is exclusive to facial procedures, and does not involve training in breast, body, hand or genital surgery, like General Plastic Surgeons. Facial Plastic Surgery is recognized as a surgical subspecilaty by the AMA and the American Board of Facial Plastic and Reconstructive Surgery is considered ABMS equivalent in Florida and throughout the United States. The American Public believes in specialization; in facial surgery, it makes sense to see a Facial Plastic Surgeon or a Plastic Surgeon who specializes in faces.
I would encourage prospective patients to use their eyes and their intuition to judge if a surgeon will be able to meet their needs. Seeing a number of surgeons is the best way to do this. Let the surgeon impress you with his/her positive qualities; any surgeon who uses as much effort in putting other surgeons/specialties as emphasizing their own attributes is deserving of wariness. In my experience, the best surgeons I have worked/trained with are true gentlemen (women) and don't need to waste their time with "trash talking".
Facial Plastic Surgery and General Plastic Surgery have a long history of sniping and turf battle issues. Both sides feel passionately about their strengths and expertise. I have worked with excellent Facial Plastic Surgeons and excellent General Plastic Surgeons, and I have seen the disasters of the less gifted of each specialty. The Bell Curve applies to every specialty.
Seek a number of opinions, listen to word of mouth, and go with your intuition.