Rorschach vs The Joker
The Scenario: In the aftermath of The Dark Knight, the Joker escapes from Arkham and goes to New York to do what he does best. Rorschach gets wind of this and confronts the Joker directy.
Round 1: Fight takes place in an alleyway in New York city, Rorschach knows about the Joker, Joker knows nothing of Rorschach except that he's a "masked hero" making the Joker think Rorschach has the same no killing code as Batman. Both get standard equipment
Round 2: The Joker is transfered to the same prison facility Rorschach is in, Rorschach being who he is will try to kill the Joker and vive-versa. Who gets the other first.
Round 3: Both of them are locked in a room with each other tied to chairs. They start talking. Who goes crazy(er) first.