“Ayurveda holds that we are thoughts which created bodies. In Western medicine we are a material (body) which creates thoughts”. This is the basic difference. So the basic reason you may choose Ayurveda is the fact that Ayurveda works on a vast expansive model which involves the manipulation and understanding of the play of consciousness and not merely matter (which is merely one manifestation of consciousness).
Traditional western medicine (and often other healing modalities also) treat only a part of the patient - the part which is considered as being ill — the material part. The Ayurvedic approach treats the whole person (physically, emotionally, mentally, socially, and spiritually) in the belief that one cannot safely split a person into parts. For example, the Ayurvedic healer may inquire into the way the person thinks, believing that thoughts manifest themselves in the biochemistry of the body. So in western medicine, after extensive diagnostics, often the disease or cluster of symptoms is isolated, and the disease becomes the sole area of attention of the traditional physicians. Triumph over that particular disease or set of symptoms is considered restoration of health. Not so in Ayurveda.
Also, Ayurveda is a natural therapy; hence it has no or fewer side effects or almost no complications (when taken responsibly and on the advise of an expert) whereas other systems of medicine often have lots of side effects and several complications.