I think, Batman takes scenario 1, 8/10. Batmans suit and environment training lead me to believe he is a better all around brawler. I also believe that Batmans cape will help to distract DD.
If Batman can disarm DD, early during scenario 2 i think he'll win very very easily. However, if he can't disarm DD within the first minute or two of their fight, i don't think he has a shot...,DD wins scenario 2, 6/10