Homeopathy is a medical system based on the belief that the body can cure itself. Those who practice it use tiny amounts of natural substances, like plants and minerals. They believe these stimulate the healing process. Allopathy is a term used by homeopathic practitioners to define "modern Western medicine" - which employs the use of drugs and surgery to bring about cures. In Singapore, the term "allopathic doctor" is rarely used.
As to the efficacy between the two disciplines, I believe that "modern Western medicine" is much more commonly practised nowadays and is backed by disease pathology, modern cures, research and evidence, especially in Singapore.
I do think that Homeopathy, along with TCM, osteopathy and naturopathy disciplines, has benefits for a small group of patients but I do not feel that patients with cancer, chronic illnesses, life-threatening conditions or patients who need surgery, are suitable candidates.