The only difference between a biography and an autobiography is that an autobiography is written by the person who is the subject of the book. Therefore, autobiography is actually a sub-category of biography. Biographies are a much broader category than autobiographies, because they are written about historical and ancient figures as well as contemporary people, and may assume a wide variety of angles on their subjects. Some biographies are written by people who were selected by the subject of the biography, while others are "tell-all" books that aren't necessarily endorsed by the subject.
Autobiographies are written by people who feel that their life stories have relevance and interest to the reading public. Sometimes this is true and sometimes it isn't. In the former case the book can become a best-seller, as in "The Autobiography of Malcolm X." In the latter case, the book slides quickly into obscurity.
Advantages of Biographies
There are a number of factors that may make a biography superior to an autobiography. First, it is more likely that the author is a professional writer and that the quality of the writing is something that readers will enjoy. Biographies also maintain a more objective tone than autobiographies, so the reader is more likely to get a story from several angles rather than only the angle of the subject of the book. Biographers often spend years studying their subjects, allowing them to provide insights into motivations and contexts as well as events.
Advantages of Autobiographies
An autobiography will always have a level of access to the subject that isn't available to a biographer, because the writer is in fact the subject. This can result in a much more intimate and revealing tone in the book, given that the writer is skilled at writing and expressing herself. Many autobiographies are written by people who were involved in historical events that transcended their personal lives, so reading an autobiography may educate a reader about history and events above and beyond the subject of the book.