Since we all know, that Aatrox has got some changes recently (and how they turned out to be), we all know, that he needs a rework. So, nothing special or intriguing or anything like it, this is my version of Aatrox, that, as for me, could find a nice place in the League.
First of all, the stats have been changed (or rather modernized), to differ them from these of older champions. These I proposed might seem to be a nerf to him (another one!), but after looking at his abilities, I hope you won't think that way.
Since old version of his trait was better (at least for me), I tried to keep it with some changes, like reducing attack speed boost and adding lifesteal boost and bonus effects to his abilities when stacked up (since it will be harder to fill the well, Aatrox will want to keep the Blood stored and fight more, granting opponents more chances to attack and punish him. BecauseI didn't like the idea of allowing him to revive only during Blood Rush not only in the middle of fight, I allowed him here to also revive outside of combat (with greatly reduced effectiveness). Since 180~120 seconds cooldown for such effect is low, I've increased it a bit.
By increasing it's range a bit, increasing it's damage and increasing airborne radius (while also reducing general radius), Aatrox should have more chances in good initiation. Since it has pretty long time till he strikes the ground, I think that buffing it won't make him broken. Also, by increasing it's cooldown, other buffs seem to be just right.
By changing damage type from physical to magic, he will be much harder to counter. Also, when his Well is stacked, he will be even harder to kill, thanks to passive free protections and escaping will be much harder, thanks to movement speed boost. Since mixing damage makes harder to build against, I had to reduce damage dealt a bit. Also, healing gained is greatly increased when on low health, but also has no base value, so theoretically it is impossible to heal with it to full health.
Changing the strange skillshot into inspiration suits him, as he was the one inspiring the losing side to the victory, awakening bloodlust in them. Since this is healing on manaless champion and it's cooldown can be reduced by slaying, it has to have long cooldown. If at 100 Blood, he will be able to cast it pretty often, allowing him to heal surrounding allies when in fight and even more when killing. It makes getting pentas for others much easier, as one double-kill will reset the cooldown of this ability completely.
A brand new ultimate that is just better (not only because it is stronger) - now he will look like a true demon of war, flying over the battlefield and slashing enemies mercilessly. With crowd-control component, he will also be able to help his teamin killing and won't be just a guy who attacks. Might be a bit too strong, but remember when I've written that I didn't decreased his stats just because!