I've played with EAP in the AttritiCon in Germany last weekend.
Unfortunately we only had 6 players and all other armies were medieval armies (Ok, one was an Early Crusader, but that was the one I didn't played against).
So I was all the 4 games facing Knights and armoured foot, so I like these enemies
But nevertheless I ended up 2nd, so also this army can work versus knights
Here is the list I played:
4 x TC Commanders
1 x 2 Guard Cavalry Elite, Armoured, Drilled, Bow, Swordsmen
2 x 4 persian Cavalry Superior, Armoured, Undrilled, Bow, Swordsmen
1 x 8 Immortals Medium Foot, Superior, Armoured, Drilled, Bow, Light Spear
1 x 6 Immortals Medium Foot, Superior, Armoured, Drilled, Bow, Light Spear
4 x 6 Persian foot Medium Foot, Average, Protected, Undrilled, Bow, 1/2 Light Spear
2 x 6 Crescent shield archers Light Foot, Average, Undrilled, Bow
1 x 4 Light horse archers Light Horse, Average, Undrilled, Bow
1 x 2 Indian Chariots Heavy Chariot, Average, Undrilled
1 x 6 Asiatic Greek Hoplites Heavy Foot, Protected, Average, Undrilled, Offensive Spearmen
1 x 6 Assyrian Foot 1/2 Heavy Foot, Protected, Average, Drilled, Light Spear, Swordsmen, 1/2 Medium Foot, Protected, Average, Drilled, Bow
Some general amendments:
You will most likely loose initiative (only a +1-modifier), so make sure you select a really large first terrain (the first terrain can be large but is counted only once) and as much terrain you can get (vineyards, enclosed fields and brushes, but if nothing is available, make it at least hilly)
You will need a any positive POA you can get, and don't meet the Knights in the open
While playing I found out that the knights are hard, but troops like Heavy foot, Armoured, Heavy weapons will be the killer for your army. On the knights you can at least have concentrated fire, which they don't like when they are BG's of 4 only, like most armies have)
The real benefit is, that you are much more BG's and you can suffer moe attrition points. You have 15 with this army, and nearly non medieval army will come with more than 12.
Use this wise and try to outflank the knights with your Cav (the Guard Cav is great in this), while they are fighting your Immortals (the real best troops you can get for your points!)
Try it, and believe me: EAP are making much fun. And it shows all the players telling you shooting is of less importance in FOG that they are wrong