Chariots superior to cavalry?
I disagree slightly with the proposition that chariots were superior to non-stirrup cavalry, at least in pure historical terms...
(1) I would argue that units like Alexander's Companion Cavalry and Hannibal's (later Rome's - after they switched sides) Numidian Cavalry would and did run rings around chariot forces.
(2) The utility of chariots was severely limited by terrain. They were next to useless on rocky, broken or marshy grounds. Cavarly maintained a higher level of effectiveness in these situation.
(3) A major reason that chariots were developed before cavalry by the Egyptians, Hittites, Babylonians and others and used for extensive period of time had more to do with size and strength of horses and the shock value of chariots against undisciplined foes than any intrinsic superiorty of the chariot over cavalry. A pair of small horses could easily pull a chariot, whereas a single horse from the same team had difficulty carrying a cavalryman for extended campaigns.
This was one of the reasons that the Celts of Britain and Ireland continued to use chariots long after their mainland brethren had eschewed them in favor of cavalry. The island breeds were fairly small...suitable for pulling chariots, but not strong enough to serve as cavalry mounts. After the Roman occupation of Britain, beginning in 43 AD, the chariot rapidly disappeared from the battlefield. The last significant recorded use in Britain was the heroic, but doomed, revolt of the Iceni queen Boudicca in 69 A.D.
(4) Tactically, chariots had many of the strengths and weaknesses of war elephants...they were primarily a "shock weapon", designed to charge enemy formations and break them. Undisciplined masses of peasant soldiers would often break before a chariot charge, leaving them to be pursed and butchered. Their utility was greatly diminished in the face of determined opposition, however.
Concentrated missile fire was very disruptive, since maiming or killing one of the horsed drawing the chariot essentially knocked the entire unit out of the battle, at least for a time. Both Alexander's troops and Roman armies simply opened lanes in their ranks to let the chariots pass through, then closed ranks and attacked them from behind using light troops and cavarly.
All that said, in a fantasy RPG, chariots (especially those drawn by creatures other than the standard horse) can make a cool addition to the battlefield

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Old One