I don't believe so. In Shogun, cavalry spears (yari cavalry) did get a bonus against cavalry. But I think CA stopped that with MTW. Spears (lances) do get higher charge values though. Some cavalry weapons (maces, axes etc) may be armour piercing.

In reality, I suspect cavalry spears (lances) were better against infantry (swords could do little against prone infantry) whereas a cavalry sword might have an advantage in a confused melee with other cavalry.