What is each man's position and what exactly is each defending?

Matthew Harrison Brady is the lawyer against the accused, Bertram Cates.  He is a Christian fundamentalist who uses Biblical support to refute Cates teaching of evolution as portrayed in a book he is teaching.  Henry Drummond defends Cates and eventually turns all of Brady's arguments against him and finally embarrasses him at the end of the story.  In the end of the story Brady dies of a "busted belly" after collapsing in the courtroom.