I and Bifi did some "testing" in the duel server today, and came to some conclusions on lance/weapon on usage for melee cav:
What weapon is best is based on the way you fight. If you like charging in fast with a courser or such, use a lance. Light lance is best for infantry, while normal lance or heavy lance is better vs other cav, though the heavy lance can be too slow. But if its "the one with the longest lance wins"-battle. (pun not intended ;)) the heavy lance might save you, but then its even better to just go for the great lance. So the conclusion on fast horses for versatile situations is the light lance. Its pretty versatile.
However, if you use an arabian warhorse or a desert horse, and play like a high manouvre cavalry man, (you keep whipping back and forth, in an out of range of the enemy) then a faster weapon is better, and the war spear has a small advantage here, since its all about hitting the enemy fast enugh. However, the light lance is able to be used here too.
So all in all I'd go for the light lance. Its cheap, good vs cav, good vs infantry and good at both high speed charging and high-maneuvrebilty-jerking. One thing to note though: if using the warspear and you have either desert horse or arabian warhorse, you are very good vs. infantry, and vs cav if you use your maneuvrebily to your advantage. AND (here is the great thing) you dont have to bring an other weapon for on the ground, which means you can have a shield while on the horse and still have a decent polearm while getting dismounted.
So, as a counclusion, I'd go for either the light lance or the war spear. Depending on the horse you have, your playstyle and if you want to be able to have both a good weapon when dismounted and a shield while mounted.