Neurology is a clinical specialty and as such, requires residency (post medical school graduate training). People who complete a neurology residency do not have a Ph.D (Doctorate of Philosophy). In this country, clinical specialties require a doctorate of medicine (allopathic or osteopathic) before entry.
In some countries, people may be granted Ph.Ds in clinical specialties but that does not translate into practice in this country or even clinical work (which generally pays better than non-clinical work). Ph.Ds without doctorates in medicine are not going to be granted clinical licensure to practice medicine in this country.
What carries more "weight" is generally in the eye of the beholder. If you are interested in research and non-clinical practice, then a Ph.D is fine. Again, most (but not all) people who earn Ph.Ds in biomedical sciences will definitely head toward research but cannot practice clinically in a specialty without completing clinical residency training.