Tactics matter, I just did 250 Sturgian Hardened Brigands vs 250 Battanian Heros, just F1, F3 with no other commands and I wiped out the archers with 176 cavalry left. Then I switched to me being the Battanians, put my archers in loose formation, backs against the red zone and on a hill with face direction and I made it out with 120 archers left alive.
My take from that is cavalry are superior if they can be given the worst possible situation they do even better than archers do when given the ideal situation.
That matches my campaign experience, where I usually wreck superior numbers by parking my archers on a hill with a shield wall in front, except against cavalry heavy armies where I can kill maybe 5 horses before they reach me and then they cause havoc on my archers behind, except I usually have 40-50 lancers and 30 or so Cav archers on the flanks to run around and kill off cavalry behind me.
Edit: I take most of that back, seems picking Sturgians for being weak was the wrong move, Aserai and Sturgian Cavalry wreck archers because of Javelins, Empire is almost even but the others all get slaughtered even on F1-F3 as me being the attacker.