Actually one gets the impression that IRL in general spears and lances were favoured against infantry, whereas when horsemen fought each other the norm seems to have been to switch to sidearms immediately after the charge. I'm guessing that has a lot to do with the habit of cavalry fights of turning into swirling melees where much of the time the opponent was very much in your face, as it were, whereas against footsoldiers it's obviously useful to be able to reach them without having to first steer your horse right into their weapons, if you see what I mean.