To beat Aatrox you need to bait out his Q and preferably his Auto Attack passive, after that you need to hard engage and reign hell on him.
Darius is a very skill dependent match up but I find Darius players who go Phase Rush are incredibly difficult to deal with. As Darius you want to be abusing your slow/auto reset to threaten his life every time he does something stupid, your Q is probably your least reliable ability against Aatrox. A Darius that gets on top of Aatrox after he wastes an E + Q has basically guaranteed him some nefty gold to spend. Also once you get to mid-late and you have armour and he doesn't, watch as he can't do shit to you and you can run him down as you please. Also a Darius who goes swifties AS WELL as Phase, well, there's no way in hell Aatrox has any chance of escaping that.
Jax is actually disgustingly strong right now and if Aatrox makes mistakes and wastes his Q, Jax can run him down into the ground and Aatrox won't be able to catch up because he can't afford to build resistances and fall behind.
In essence, Aatrox is an oppressive champion but he's not without total weakness. He has no resistances and is very vulnerable to a hard engage after wasting his abilities (his cooldowns are SIGNIFICANTLY long so abuse his ass when he wastes stuff! also he only starts with 1 dash early, if that's gone and he's in a bad spot, you can mess him up real good). He can't trade back against divers with attack speed because his attack speed base isn't fast enough to do anything, for every 3 autos Irelia can do to him, he can only do 1 back at best and that's not a good spot to be in.
Good luck amigo, spam norms or match ups against him to earn the experience of how to play against him and one day, he will be no more than a fart in the wind. Know yourself, know your champion and know his cooldowns, the rest is taking the initiative.
[slayer-pantheon-thumbs]