Let's examine the tactical elements that govern military encounters:
Local superiority(LS) - local superiority is the most basic, and most decisive principle. It does not matter if you consider a clash of large armies, or just a bar brawl (when you are about to punch someone's face through his skull, and someone you didn't see smashes a bottle against your head from behind - that's the case of local superiority). LS principle arises from the fact that it's extremely difficult to fend off attacks coming from multiple directions (both in melee and ranged combat). The greater the angle of the attack vectors, the harder it is to defend.
Maneuvering - every maneuver is just an effort to create local superiority conditions against the opponent while trying to thwart the enemy's effort to achieve the same. Larger army will try to wrap the line around their opponents shorter line, to destroy the flanks by LS. The enemy will try to counter by withdrawing to a defensive position, where terrain disallows this (mountain pass, a ford, city gate, etc). Elite units may try to smash through a point of weakened enemy line, and destroy parts of the opponents lines by attacking from behind.
Formations - formations are tools specific to certain situations, designed to maximize the possibility to achieve local superiority while denying the opponents to do the same. A large army may adopt a crescent moon formation to speed up the process of wrapping the enemy lines, applying LS to the flanks. The weaker army, seeing this, may adopt a circular formation, thus enabling the opponent to apply LS on every point of the formation, but with lesser effect (the angle is smaller, noone gets attacked from behind). Higher quality troops can cause enough casualties to a larger, less trained and disciplined army this way. There are two, contradicting qualities of formations, forcing the general to make difficult choices. Wide formation is less prone to being flanked, but can be punched through more easily, while deep formation is more easily flanked, but the line is more difficult to breach.
Formation structure - unless we are talking about a brawl of identical, primitively armed units, armies always have a structure. Heavily armored frontline protects fragile, but powerful ranged and artillery units. Siege engineers can negate or lower the advantage of the enemy fortifications, but must be protected while they do their work. Supply lines and caches must be protected, if the army expected to fight with peak efficiency. And finally, loss of a vulnerable, but critical command units can throw the whole army into a disarray. These considerations bring another layer of complexity into battle plans.
Morale - morale represents the ability of the individual soldiers to disregard his/her personal safety and instincts and work coherently with the rest of the army on applying the predetermined battle plan. Some aspects are obvious (i.e. not running away), some are critical for certain phases (is the unit able to hold a ladder to enemy fortress wall while hot oil pours from above? Will the heavy infantry hold the line under a barrage of enemy arrows, while catabults they protect demolish enemy walls?). Morale can be context-dependent and can create interesting relations in the whole army structure - seeing a renowned champion fall, breaking enemy line, or just losing flag bearer that signals commands to a whole unit.
Most successful games implement these principles to a degree - most notably the Total War series (rather poor AI aside). On the other hand, omitting them leads to loss of dynamics that is characteristic for military encounters.
