They milk more drama out of Batman than they do Superman or just about any other DC character.
They've done horror, sci-fi, crime noir, psychological, historical, Westerns, pulp etc. with Batman because they can get away with using him in a lot of those themes. There are shades of grey to Bats.
They don't do many with Supes because they tend to view him in Black and White. Good Superman or Evil Superman.