Well heavy cavalry doing well against infantry of the past ages makes sense since basic infantry were mostly fodder.
Just in Medieval times. I definately would not like to fight hoplites or the roman legions, both of whom were very effective against cavalry
Well Elvenlord mentioned that heavy cavalry was used to mow down infantry in the past quite effectively. As far as I know it was only during the Middle Ages. Your right in that during antiquity that armies consisted of more powerful infantry and cavalry was weaker(lighter) and less extensive. Even the weak cavalry aside the heavy cavalry wouldn't do much better since the infantry mostly used spears and had considerable armor and training.
I think the dichotomy should be simple. Heavily armored cavalry are more for being in the thick of things more like beefier regular soldiers. Medium cavalry is there for mobility and flanking. One is clearly designed to be used for trampling while the other isn't. Heavy cavalry is mainly used to crash into an army and start hacking away. They aren't good for trampling from a realistic view since its difficult enough trampling, but speed and maneuverability is less with all that armor. It doesn't matter how armor may add weight it detracts heavily in the ability of the horse to move as effectively at higher speeds. Especially with the high center of gravity plus armor makes balance a serious issue and even more so when trampling. Once that heavily armored horse goes down its less likely to get back up so the rider knows not to compromise themselves. However, the impact should be far greater since the point of heavy cavalry is more about damaging than routing or mobility. They have a bit of the strengths of cavalry and heavy infantry which makes them unique.