doesn't it kinda depend on which horse archers you're facing too? I remember reading somewhere that the horse archers in the Saracen armies used a light bow that wasn't so effective against the Crusaders. But the Mongols used something that hit a lot harder, plus they were organized and well disciplined far beyond anyone they faced in Europe...
Actually yes, the Mongols first defeated and conquered virtually all the nomad steppe tribes/peoples. And that makes us think that the Mongols were much better than any other nomad tribe/confederation.
So an idea that "any nomad army is equal to any other nomad army" is painfully wrong.
It is the same as saying that there is no difference between sedentary armies; like "an army of the Cimbri and Teutons is the same shit as an army of the Roman republic - just foot soldiers with swords, spears, shields and a little bit of cavalry."
* But the Mongolian bow being better than other nomad bows is an old myth. The Mongol bow was exactly the same as the turkic bow used at that time from Bulgaria to Uiguria.