Unique Aatrox Buff!
I got it! Don't change anything about his game play mechanics. (except make his blood well drain slower please)
Aatrox loves combat and loves uphill battles.
Therefore, when the enemy teams has more kills, the challenge invigorates him granting him a buff per score difference.
It could be like 1% increase of ALL stats per difference in kills. So if the enemy team is up by 5 kills, Aatrox will enjoy a 5% AD bonus, AS bonus, Movement bonus, life steal bonus, tenacity bonus, AP bonus, health bonus, armor bonus and MR bonus.
Or you could regulate his bonus to just AD, AS and Lifesteal.
You get the general idea.
I think this would make Aatrox very interesting. A snowball dependent champion who has a chance to turn things around if his team is failing him hard.