the worst combination is Cataphracts and Horse Archers. Under a good commander they're almost unbeatable. You can't put your legionaries in testudo, or their cataphracts jut charge is. So what I'm forced to do is put my army in a square, holding my cavalry south of the square (idea being to lure thier cataphracts to chase my cavalry over the field
allowing me to put my legions in testudo) I make sure I have lots of archers (I prefer cretan archers, but since you can't get them in custom battle, I try to survive with auxilia archers). Once the enemy horse archers run out of arrows, they can usually be hunted down with ease. But the most important thing to do is put your troops on guard. I was fighting parthians and did this, and when their cataphracts charged, they routed; but my overzealous troops broke out the square to chase the enemy. The result was that they brought more cataphracts in and charged through my square's gap to my archers-and my general, who was killed. Thus my whole army routed in terror.
I should add that keeping a close hold on your cavalry is essential. Use controlled charges to keep them away from your square, but don't pull a Publius Crassus and go to far.
His ego nec metas rerum nec tempora pono:
Imperium sine fine dedi.
(P. Vergilius Maro, Aeneid I. 278-79)
We are all, so far as we inherit the civilisation of Europe, still citizens of the Roman Empire, and time has not proved Virgil wrong when he wrote nec tempora pono: imperium sine fine dedi.
(T.S. Eliot)