A lot of the discussion already posted is very good. Some, or most, of what I will say has already been mentioned.
1. I believe tht the richness of different types of magical attacks should be included. It would add greatly to my enjoyment of the game. This would allow unit specialization and uniquness of units from cities, regions and empires based on the magic and production facilities in the city, the environment in a region (swamp, tundra...) and the Soveriegn of the Empire.
For example: If I am raising units in a city with a type of magic node, then those units would have some of that type of magic. When they fought units of the opposite type they would have greater damage, and perhaps take greater damage as well.
2. I believe that different typs of physical weapon effects can be modled with a single physical defense stat that is modified by type of armor. For example, ring mail could give less defense to a piercing weapon (epee or arrow) than it would to a cutting weapon (cutlass, sabre).
3. Experience gained in battle is very important. Training is insufficient to gain more than the lowest levels of experience. Experienced units ought to have better morale, damage potential and abilities. These abilities could be both offensive (types of attack) and defensive (new formations, such as forming a square against cavalry).
4. Technology advancement could open up both new types of items (epee instead of broadsword, platemail rather than leather) and improvements in tactics (longbowmen learning to place sharpened stakes in front of their positions to stop cavalry charges).
5. Unit morale should be an important factor. It can be improved by experience, good leadership, Soveriegn traits, perhaps by magic, by success in the current battle, fatigue and other similar factors. It can be decreased if nearby units route, if leaders route or die, thru fatigue and most certainly by flank or rear attacks. Also, summoned creatures, undead, being outnumbered vastly and also enemy magic might influence morele. Units ought to be able to break and fell, perhaps rally and return, etc. Various games model this behavior different ways.
6. Terrain ought to be important to tactical battles, as has already been hinted at. High ground, defending behind a stream or swamp, hidden in woods or behind hills should all be relevant. Magic attributes would also be relevant, water blessed units defending in a swamp are better, fire units attacking across a river do so at a disadvantage.
7. Battlefield movement is important. Early in the thread the example of Mongol cavalry mobility was mentioned. One of the 'special' abilities of experienced cavalry could be not only additional movement but the ability to move, fire, and move again. Units ought to have directional facing, if attacked from the side or rear they ought to suffer disorganization and morale loss. If attacked from multiple directions at once it ought to be more severe. It ought to take time to change direction, though more experienced units ought to do it faster and leaders could incluence this.
8. Battle awards/medals. If units can be renamed, the player could add self-defined rewards to the name by adding * of ^ etc. However, I think it would be a neat feature to have different medals ingame that the player could give units, either through specific presentation to the unit or through user defined criteria. For example, if a small army wins against a superior foe you could give a 'Kings Medal of Valor' to a unit. And/or, each time one of your units has fought in five battles it might automatically be given a 'Chevron of Experience' on the sleeve of their uniform. These may not actually change unit traits but would add to immersion as the player becomes incrasingly fond of favorite units.
Summary: Whether optional or required, the ability to have tactically complex battles is probably a strong draw for a great many potential customers.
Thanks for letting us give so much imput!