Such as, Light Cavalry, Heavy Cavalry, Missile Cavalry, Light Infantry, Heavy Infantry, Spearmen, Missile, ect.
It's all about the positive waves, man.....
Well, heavy always whoop up on light units, unless they have to cover a lot of ground to get to them. Once heavy units get get 'winded' the wear out quickly. Light units can take them out pretty well then. Light horse are great for running down just about any other unit that routes, especially heavy horse and bodyguard units. Spear are just dandy for taking out horse, but won't stand up to a frontal charge well. Not that any foot unit will.
In my opinion, it just depends on the current battle. Heavy cav is good for smashing lines or the occasional drawn out fight. Light cav (those with Fast Moving trait) are great for taking out missile units or running down routed cavalry. Horse archers and jinetes are also great for softening up larger armies before you attack.
Infantry is good at taking out other infantry and spear as well as taking castles. Spearmen are good for taking out horse. Archers are pretty limited in my opinion, but higher end crossbow and gunpowder units are very nice. I'll route at least 2 units before they even reach me with a couple of units of either of those. (in open terrain)
Generally if you utilize a unit with it's strength in mind, its:
Cavalry > Non-Spear > Spears* > Cavalry
Armor Piercing ** > Non-Armor Piercing
Infantry Archer > (at range) > Mounted Archer > (in melee) > Infantry Archer
Armor Piercing Archer *** > Gun Powder > Crossbow > Archer
* which includes any unit that specifically says they get bonuses fighting cavalry
** which includes javelin units like Jinettes
*** Example would be Scots Guard
Heavy Cavalry's main advantage is their charge. On the field they dominate. In settlements they are less useful. They obviously can't go up on walls, and unlike Medieval 1, you can't dismount them before battles. Once they enter melee, get them out and line them up for another charge.
Light Cavalry with Gold level experience, although they don't have the crushing power of heavy infantry, can still do a reasonable amount of damage.
Non-spear infantry can't stand up to a cavalry charge, but hack spears to bits. You generally want to place non-spear infantry in the back row, unless the enemy brings no cavalry with them, which in that case put them in the front so they come into contact with the enemy infantry first.
Infantry archers tend to have longer range, more ammo and more accuracy than mounted archers, but they are susceptible to mounted archers if the mounted archers decide to charge and go into melee. In a stand-up ranged battle though, infantry archers will deal more casualties.
Armor Piercing archers have the advantage over gun powder because they have the range accuracy and rate of fire compared to gunpowder. I remember one battle where I charged in a squad of cavalry who got cut to pieces by several squads of Scots Guard.
Crossbows and Archers tend to be relatively matched. The crossbows slow rate of fire is compensated for the fact that they hit through armor. I've had several battles where my crossbows kept up with the archers for kills, if not exceeded them. Early on when armor is not as frequent, infantry archers are just as good. Eventually though you will want to invest in crossbows, as more and more armor hits the field.
I've heard that Gunpowder bypasses practically everything except armor. Consider all defense stats except Armor to be 0, whereas Gunpowder (like Armor Piercing) cuts the armor stat in half.
To be successful on the field, you need to know what your enemy is bringing to the battle, and make sure you have the units that trump theirs. Always good to know what kind of troops a faction tends to use, so that you can gear your training facilities to take advantage of the composition of their armies.
As the late game English, beefing up your army with Yeomen and Retinue Longbows can mean utter devastation wrought upon your foes in any battlefield. And I don't know if it's just the English cavalry, but whenever I have my English Knights or General's bodyguard charge a line of opposing Feudal/Dismounted/Chivalric knights (or other equally heavy infantry) they always get completely owned by the foot troops. In my current campaign, I kept getting harassed by Spanish and Portuguese invasion forces(who formed a kind of bloc with France just to fight me) even as far as Carnaervon, so I sent my best general with a full stack of elite, expensive troops to take Pamplona, which I figured to be the main Portuguese staging area. It's been at least 70 game turns since I took the fortress, and I haven't moved my army from there. From defending the waves upon waves of Iberian troops, I've learned to only command my mounted units to take down fleeing troops. I've also learned that archers, whether they are Archer Militia or Retinue, are indispensable during a siege and, when massed, will usually devastate an enemy army even in open battle.
Another note about archers..
If they are in direct line of sight to their target and there are no friendly troops in front, their arrows will fly straight into opposing formations. The alternative to this is the arching air shot, which is always wildly ineffective compared to the brutal shooting they are capable of with direct fire. You can boost your effectiveness with archers to a great degree if you can position them correctly. Even Archer Militia are extremely deadly if you can maximize their firepower.
There are also fire arrows for archers. If you have very weak archers like peasants, using fire arrows is a sure fire way to squeeze some damage out of them at the cost of lower rate of fire which can make them effective against stronger forces if you can keep them at bay.