One difference is that “what” can be appropriate when the choices are unlimited, and “which” can be appropriate when the choices are limited. “What is your favorite character” implies “in all books and movies ever made.” “Which is your favorite character” implies “in a particular movie or book.” Other examples: “What is your favorite book?” [answer can be any book]. Compare to: “Of the Harry Potter books, which is your favorite?” [answer is limited to one of the Harry Potter books]