Classic newbie case of the "Last invincible cavalry squadron" :
1) you attack without maximizing the flanking bonus for your cavalry, thus losing in attack strength potentia, lengthening the fight and losing more morale than you should in the field battle (you had only 60% of your cavalry in flanck, it should be at least 90%)
2) you attack in plains, thus giving 20% bonus to ALL cavalry ... and your sopponent has quite some : even with less overall cavalry, he manages to have almost as much as you in the flanks
3) you have relatively few phalanxes .... phalanxes are both the bane of enemy cavalry and the killing booster of your own : they are cheaper and quicker to recruit, yet are on par against cavalry when opposed to each others (3 spears against 1 cavalry, the spears win : 1 is dead, 1 is cured, 1 survived ... much cheaper than to lose the cavalier) ... and due to their numbers, they help put more of your cavalry in the flanks.
... which results in having your opponent's cavalry surviving in the flanks while decimating your footmen and innflicting more losses on your side than on his, thus making you lose more morale ... just look at the details of round by round details of the field battle : after the first destructive rounds, you just can't get to kill his cavalry for 11 f***k rounds !!
now re-simulate the same battle with 30k more phalanxes and 10k more guardians (for the anti-spears/anti-archers punch) ... and tell us what the battle simulator says on average