I thought about this because they bith view the violence they cause as art however Aatrox's killings set huge wars in motion while Jhin's inspire fear and lunacy.
Aatrox reminds of Ares, a god who thrived in war because of the thrill of battle and bloodshed. Aatrox doesn't seem like a guy who kills out of some obsession or desire for "art;" his champ select quote imo is just a figure of speech.
Jhin on the other hand kills out of a sense of obsession and addiction; It's where he finds his purpose. Jhin kills in artful fashion because it's all he can do to feel satisfied and alive.
If anything, Aatrox would likely be disgusted by Jhin's selfishness in killing or his reliance on it as a crutch for his own personal satisfaction. Aatrox views things in the scope of war, not death itself. He lives for the thrill of battle and the fury of war, something Jhin neither exhibits nor has ever experienced. Aatrox states that war reveals what is within us, and I'd imagine he wouldn't be pleased with what he found in Jhin.
Jhin would likely view Aatrox with contempt because of the crudeness of his work in battle. Among other killers in Runeterra like Draven, Zed, etc, he shows little respect or admiration, most likely due to an aversion to the lack of craft and artistry they show.
Just my thoughts.
I think it's more of a fine line than simply that.
I believe Aatrox sees war and killing as art where as Jhin sees art more so in death than in the killing itself.
To use an Aurelion Sol taunt: "You bend time the same way a child folds origami. Cute, but nothing special". I figure Aatrox would perhaps see potential in Jhin's artistry, but might be like "eh, not all that special or worthwhile", or potentially he'd have issue with how much Jhin seems to care about the form and manner of killing. Perhaps he's too meticulous about his craft; he examines things to carefully, and doesn't make broad strokes like Aatrox does.
