If the team should decide that they want two types of mounted units they should really be less similar than they are now (as others have already suggested).
Oh, and please think about not making that second path "chariots". That is the horsey equivalent of putting Arquebusiers and Gunmen with Winchester rifles side by side - it is just silly.
A popular scheme in other games is having a horse archer line and a regular horseman/knight line. Maybe the horse archers could be the skirmisher types while the knight line is more "tanks with four legs".
Agree completely with the above. Regular chariots are fine, but war chariots are too similar to knights from a gameplay perspective, and just silly from a historical/lore perspective. Mounted units need a second national unit that's well differentiated from knights gameplay-wise (and, please, NOT a unit that was obsolete for thousands of years by the time knights were around). A new horse archer unit would do well, perhaps they could have lower strength but get terrain defensive bonuses - or higher base strength, but not benefit from weapon upgrades - and/or bonus vs. melee units (historically infantry had a difficult time with horse archers that could ride away while firing back at them, the infamous "parthian shot") - and/or much higher withdrawal chance. Really, anything that makes them significantly different but not always better than knights.