Keep in mind that on "Hard", the AI troops get bonuses. Thus two units of equal type, weapons/armor bonuses and valour will not be equal on the field (the AI unit will usually kill many many more of your guys than your guys would).
To see this for yourself, take a unit type, and set up a custom battle. Give the AI and yourself the same unit (pick a faction for the AI that has that unit of course). In the combat, simply tell your unit to attack the other (no flanking or other tactics). Watch the results. On medium, about equal numbers on each side die and it's a tossup as to who routs first. On hard you will lose 9 times out of 10, and lost twice as many units before your troops break (at least in my tests).
If you want a fair fight, don't fight "hard" battles. I have no idea if the AI's tactics are different on the higher difficulty levels. My preference would be to separate tactical AI from unit stats boosts. I want to play against the best tactical AI possible, but with equal troop stats (for otherwise identical units).
Try the battle again at Medium. If the battle was tuned to be very difficult (but not impossible) on Medium, then you're very unlikely to win on Hard except through luck (or figuring out some tactic that gives you a huge edge).
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