Countering byzantine Cataprachts + where to find unit bonuses

So I just played vs AI which dominated me with Elite Cataphracts.

He went almost pure Cataphracts, and since its cavalry I thought I could make Halberdiers and simply crush him that way.

This worked out terribly. It seems there is some bonus for Cataphracts against my halberdiers. So this brings some questions:

1: Is there information in the game to find about these bonuses? I can't seem to find anything.Or is the game logic that one is simply supposed to 'just know' things that there isn't information on in the game?

2: Another thread said to used ranged units against them. But as far as I could see they had even more armor against ranged units than pierce armor. So what should I have done ?

(playing HD version today, but I play both)