Who would win in a fight, Him or Aku?
It depends on the story. The plot, the theme, the reason they’re fighting; all affect the outcome.
My general opinion is that Him plays mind games on a level that Aku cannot even begin to, like playing chess with someone who only knows checkers. Something like Him, who preys and feeds on negative emotions, would have a serious advantage over Aku in this regard; his hate, rage, fear, and sorrow are beyond mortal comprehension.
On the flip side, Aku is more powerful physically/supernaturally than anything in the Powerpuff Girls’ world — because in that world, the PPG are the strongest, but Aku is the source of Chemical X and more powerful than them.
So it’s not just a simple “well x could beat y because” answer, there are a lot of different factors to balance.