Here's what I found:
Cav vs Spears: in SP I faced a full general's unit (30) with just one unit of spear militia in city combat. On the initial charge, I lost about 20 spearmen, but after that, the cav was butchered. In the end, I had about 50 of the original 112 spearmen left, and, considering they are low-tier, that kill ratio is amazing IMO. --> on the charge, cavalry is adequately powerful even vs spearmen, but once they are stayed, they die very quickly.
Cav vs cav: in MTW and Rome, I liked doing pitched all-cav battles in custom just for the looks of it. Having two cav armies charge at each other looks just plain cool.

In MTW2 I found that cavalry units have problems charging each other head-on: In Custom Battle, I set 1 unit of Teutonic Knights vs 1 unit of Hospitallers. When I ordered the head-on charge, my unit stopped just before the impact without any apparent reason. As the enemy cav continued their charge, they killed about 10 of my knights while I killed none!
I hope they fix that...
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