Re: defeating cataphracts; while I endorse the horse archer advice for Parthia, I actually had a surprisingly easy time with Armenian and Parthian cataphracts as Seleucia, in part because I tended to fight defensive battles. 1 on 1 I'm sure no single phalangite is going to have very good odds, but I massacred them with militia hoplites simply because you get so much phalanx for your money; and because I dragged them around with jav cav before leading them up a hill to my infantry, at which point their performance weren't so impressive. (Still good, but surely not cost effective, especially against militia hoplites and eastern mercenaries)

There's perhaps a question of what is and isn't cheesy vs. the AI - using terrain, using corners, using cavalry to disorient them - but ultimately an amount of gaminess is part of the game, since to maximize the ai's intelligence would require you to play with somewhat boring and routine tactics.