Cavalry vs. infantry has been one of my major toothaches since I bought civ3 (got an early not-so-legal version when I was visiting russia, month before it was possible for me to buy the real thing - which I did btw). Civ2's way to portray war was much better in many ways.
I think Kryten's view is more than just but it seems nobody is wrong here. It's things like the way AI uses units (and makes the player use them), the way different branches of arms have been separated and finally that it's sane to put million units in the same stack in civ3, which will make it hard for the game to portray the actions of a battlefield realistically.
Without a question mounted troops as arms have played a major part in battlefield and will continue to do so. Their purpose however can be divided to different roles, to view their behaviour troughout the history:
1. Mounted warriors rode to a combat zone, dismounted and marched on the battlefield to fight on foot. In this case the only advance of being mounted is strategic: fast movement of the unit. Modern equivalent is the mobile infantry - mech infantry comes close with the difference that their horses are mighty aggressive. In the Middle Ages in Asia quite similar formations did exist - mounted archers, cavalry with spears and swords plus light infantry units were used as shock formations. These were mobile troops which could react fast to enemy maneuvres on the battlefield - and save a day.
2. Chariots (probably the oldest) acted very similar to tanks - both in support and assault roles. It is a usual image that on battlefield hordes of chariots charge on infantry which starts to fail when it seems the fast moving menace. Other image is that two armies of chariots fight "in duel mode" with swords in close combat. These situations have taken place more in films than in reality. Due to the high cost chariots were often limited to few which operated to support infantry - while supported by infantry.
With slight changes knights and heavily armored cavalry were used in the same way during the middle ages. They were like early tanks, hard to wound but alone very clumsy, slow and wulnerable. Knights were all the time defended by the footmen, which made it easier for them to wound than get wonded and were able to draw the attention of the enemy on themselves - thus acting as points easy to distinguish from the action for the leader. This is how tanks were used before modern mobile warfare was introduced, and are used even today.
3. The purpose of cavalry itself is to support infantry. This can be seen by staring at numbers - a cavalry regiment is small, few hundreds, compared to an infantry regiment, can be thousands. Cavalry is always very expensive, their elite status is result of long training and high upkeep. Never it is a good idea to frontal assault the enemy infantry with even a tiny bit of cohesion, because it will cost money and expert men.
Cavalrys most valuable weapon is maneuvrability, which is a important factor when surprising the enemy. It can be easily used to harass artillery and to hunt escaping enemy footsoldiers, with some consideration to flanking mission and then it is better to keep the enemy occupied with something else, so the cavalry can flank in peace.
Cavalry plays an important role but infantry fights the battle. You can't attack to cities and forests with tanks without infantry cover and it was the same then. Places are narrow and tanks are blind and clumsy. Only soldiers on foot can be used against even highly fortified positions effectively. Can't imagine tanks or horses capturing houses or bunkers, riding uphill assaulting against lines of infantry aiming calmly at them.
Of course history is filled with exceptions but these are single battles, often fought in small numbers.
Then to another thing: "Bozo" tactics were sane at the time. Armies at the time lacked proper communication devices and weapons had to be loaded while standing. If the other guy used massive lines of musketmen and later riflemen backed by the artillery there's no way you can make your guys to attack fighting independently jumping up and down thinking about good moment to load the weapon. Guerilla warfare was a great idea, but it's effect to the outcome of the war is usually close to insignificant.
Bozo tactics were of course perverted compared to modern standards, today every life seem to be valued (but is a target nevertheless). It wasn't like that then, death in combat was a part of soldiers profession. Officers had honor codes, mainly because it was thought that there's no need to spend more lives and property that war usually demanded. Wars at the time costed thousands of lives, perhaps a some hundreds of thousands in total in Napoleonic wars. World War II took 50 millions in much less time. In my mind there's some idea behind the honor code. These days it's just about bombing from miles away. As George S. Patton said: "Where's the honor in that?"
So to be in-topic I'd have to say the infantry should have at least the same attack strenght than defence, like Kryten suggested. Perhaps cavalry should have more movement points and artillery more range. But the game remains unrealistic because of limitless stacks. I've also been thinking about making railroad unavailable just to make wars more interesting.
Wake up, it's over!
Ukas