I have a broken fibula and facing surgery or leg cast for 6 weeks. what is the healing time of surgery and what are benefits of it over the cast?

Better results: The results that you can receive are dependent on the extent of the injury that you have. You are young and pending on the type of fracture (aligned ?, stable ? Involving the joint ?) all come into play when deciding if surgery is better than cast. That being said, in general surgery has a better shot of providing a better out come. Your surgeon is in the best position to advise you.