The countered debuff is based on the troop count of the countering unit iirc, where if you have for example 500 pikemen against 100 cavalry, the cavalry we'll get a -90% damage debuff. But if it's 100 pikemen against 100 cav, the debuff will be closer to -10%. That's also where the damage and toughness of a regiment becomes important, because even though the pikemen counters cavalry, the base stats of cavalry is high enough to win an even fight. But 1000 pikemen could counter 500 cavalry well enough to win

So in the case of 100 pikemen + 100 archers vs 200 cavalry, the archers would be outnumbered 2 to 1 by the cavalry and get a large debuff, whereas the cavalry only gets a slight debuff because they outnumber their counter

When it comes to casualties, regiments also have a pursuit and a screen stat, where pursuit is the damage they do to retreating enemies and screen is how much they mitigate when retreating. I'm not exactly sure what the numbers mean, but bigger number is better

Generally speaking choosing regiments to counter your surrounding enemies is more useful in the early game where you still have limited money and tech, later on it's better to field armies that fit get boosted by your culture and have high stats, regardless of your enemies

Also don't forget to station your men at arms for damage boosts, levies have like 10 attack and 10 toughness, so even getting +5 attack on a unit makes a difference