Their personalities are so different. Aatrox's quotes just sound more mature than Rhaast's. Basically, all that Rhaast wants is destruction, murdering and chaos. While Aatrox wants victory and doesn't sound so violent and hostile (he is, but you know).
At some point on Reddit it has been stated by a Rioter that Aatrox was kind of the leader figure of the Darkin when they used to be free So as a leader he probably has a more chill personality Rhaast is described as pure evil in Kayns lore and after being freed after ages he now sees his chance to rise to the top So he himself is actually alot like Kayn who wants to be better than Zed.
I'd assume its because Aatrox has been 'free' for sometime now, opposed to Rhaast who is still in his weapon/ just got out (if you transform into him in game).
Aatrox doesn't want victory,he wants bloody wars,where lots of people are dying.
He is a bit like Jhin in that regard,only that jhin sees the deaths of his victims as his art,wheras Aatrox sees a big war,where lots of people died,as his art.
So basically Aatrox glorifies his misdeeds,wheras Rhaast knows that he is a killer and doesn't try to justify it.
And the irony is that Rhast is doing what Aaotrox should be doing and feeling
