Is a psychologist or psychiatrist better for a career with the study of the mind and phobias?

Phobias: Psychiatrist with special training & added qualifications, that does medication management as well as psychotherapy.

Both are good: If you're interested in social behavior and social sciences, psychology may be for you. If you're attracted to the basic sciences, (biology, chemistry, etc.) and don't mind a long educational journey, medicine and psychiatry might be the ticket. Fwiw, most psychiatrists made the decision first to be a physician and secondarily to be a psychiatrist. Most psychologists knew in undergrad studies.

Both : Both our careers in the study of the mind of which phobias are a part. The key difference is whether or not you wish to prescribe medication. If you do then go to medical school and become a psychiatrist. If you do not then get a PhD or a PsyD in clinical psychology.