I think the two can complement each other pretty well because they usually serve different purposes. A psychiatrist can evaluate symptoms, consider whether medication makes sense, and monitor how treatment is going, while therapy gives you a place to work through thought patterns, stress, behavior, relationships, and the things contributing to the symptoms. For anxiety and depression, both therapy and medication are commonly used, either separately or together, depending on the person and how severe or persistent the symptoms are.
For some people, therapy is enough. For others, medication makes a noticeable difference but doesn't really address the underlying habits or situations that keep triggering the problem. Having both providers can also be useful if they communicate and are working toward the same goals rather than giving completely separate advice.
If depression continues despite standard treatment, a psychiatrist may also discuss other options, including brain-stimulation treatments such as TMS. Information about
https://lotuspsychiatryandwellness.com/tms-boca-raton/ is worth reading if that situation ever comes up, although that decision would really need to be based on an individual evaluation.