Better Argument is the personification of a more traditional mode of philosophy and instruction that had previously held sway in learning. Well, we say traditional, but Worse Argument uses the word "moldy" (919)—potato, potahto, right?
Better Argument is, as his name would imply, better than others (i.e., Worse Argument) and preaches "what is just and fair" (900).
He's pretty physical, though (and he thinks that being physically fit is pretty important)—to the point where he's not above threatening Worse Argument with physical violence.
Also, he doesn't seem very resolute or solid in his principals: he actually says he's going over to Worse Argument by the end of the play. Bummer.