Quote Originally Posted by Korlon
I would think the lance or spear would be better off against cavalry as well due to the bonuses it gives against them. And, of course, use the secondary against light armored troops. Generally, the lance has some waiting time between blows, so it'll kill lightly armored troops slower.
Lances have a very low attack value and a long attack delay, so they are only useful in a charge. They do have AP, but most lance-wielding cavalry have an AP secondary weapon as well.

Spears do give a bonus against cavalry, so there may be an advantage in not switching to secondary weapons in a cavalry fight. I haven't tested it, though. Also, several eastern spear-wielding cavalry units have an axe as secondary weapon, which would give more bonus against heavily armoured cavalry than the spear does.