Human players always win in heavy cavalry duels, it only matters a little if the Human's side are inferior. I had an amusing experience in my KH campaign, when my 800+ (don't remember the exact number) Hippeis and Hetairoi Aspidophoroi fight versus full stack army of Sauromatae cavalrymen... at first I just think to launch a desperate attack into their heavy cavalry flanks with all my hippeis... and I was shocked when most of the Sauromatae routs first after long bogged down hand-to-hand fight (their HA joins the mounted riots too)

I win because the AI is too stupid to let their heavy cavalry drawn their secondary weapons, rather than 6 damage pointy sticks they used to charge... ... both armies are on captains