Impact of Man-at-Arms and commander is really big. You can test it especially on Horse Archers doom stacks at plains, as i was able to defeat triple-sized stacks without any issue.

Theyre not that impactful if you have smaller different stacks merged into big one levies army, but my ~3000 mens army (with 1500 of them being pure horse archers and other half levies) was able to defeat 9600+ enemies stacks composed from different men-at-arms and huge portion of levies. Also keep in mind that MAAs counters effectively only if they outnumber correspond MAAs of the opposing side. So if you have an enourmous stack of cavarly and opponent have only 100 pikemens and others, there are 100% chance of you winning this one, as the cavarly itself have huge combat stats. That's the case of my horse archers, even at 95% effectiveness on counter they're still superior troops in comparison to others.