Kingdom of Heaven refought (different commander)

Instead of Balian of Ibelin leading the defense, it is Aragorn (from Two Towers). He has only 1 battalion of Elves against Saladin. Does he win the battle or does the city fall?

I don't believe anything could've gone differently.

Saladin couldn't beat Balian's army, it would probably be the same result if Aragorn was leading them instead.

Unless you mean just one unit of elves and nothing else? If so he loses, duh.