From what I pikced up from watching Damon's Inside the Actor's Studio edition, Damon had the whole story other than the ending written and much of the vital dialogue planned for Good Will Hunting, and Affleck's role came in after Damon was told to keep working on it by his professor. All Affleck truly did was help Damon steer the story towards an ending and some other scenes between Will's friends.
So it's still mostly Damon's beast, and he deserves more credit than Affleck.