When it comes to cosmetic surgery of the head and the neck who does it best?

Do your homework. As with any cosmetic surgery, do your homework. Look at on line reviews -/+. Ask other patients. Cosmetic surgery is both art and science; but art is most important. Look at before and after images. Certification, experience can guide you in your decision. Choose well. Most can get a driver's license, yet not everyone can drive. Certification is important, but experience and outcomes are more..
No one simple answer. These operations are done by plastic surgeons and facial plastic surgeons. The difference: plastic surgeons have prerequisite training before their plastic surgery residency in general surgery. Facial plastic surgeons are first trained in otolaryngology (ear, nose, throat) before their fellowships. Both can do an excellent job. Do your homework about each surgeon you are considering.
What board? Check what board a physician is certified in first. Plastic surgery board certification requires 2 or 3 years of plastic surgery training after 3 to 6 years of general surgery. Facial plastic surgery requires 1 year after an ENT residency. Cosmetic surgery board requires less time specifically in cosmetic surgery and the initial training can be in a variety of specialties.
Depends. Regardless of how they are trained, any specialist can be good, or not so good. Talk to your primary care physician, or friends you know who have had cosmetic surgery. Also do your research on the internet.