I use cavalry primarly armed with overhand spears or (better yet) swords, for chasing routers. All of these guys double as skirmishers early in the fight too:

My favorites:
Daha Rog Baexdzhyn Aefsad (Dahae Skirmisher Cavalry, armed with axes, but kind of pricey)
Hippakontistai (Hellenic Skirmisher Cavalry, with armour piercing swords, [the kopis right?])
Hippeis Tarantinoi (Tarantine Elite Cavalry)
Marholeudiz Wolhiskoz (Celto-Germanic Cavalry, armed with longswords)

I believe they have a faster "attack rate" or something than the lance armed guys. This and other values rely less on charges and more on the weapon itself.