In my Turk campaign (TLR Mod) I find a stack of Saiphis (sp?) works very well against the Mongols. You'll take alot of casualties but you'll also decimate a Mongol stack.

When it comes to western factions bowmen (like Longbow men) works better against Mongols than crossbow men. Crossbow men usually have better armor but they are slower to shoot and have shorter range. Also if your bowmen can plant stakes its especially helpful against mongol mounted troops.

I find mounted archers like Siaphis to be the best so far but not the only way to defeat Mongols. So I'd say Turks and England are the two best. I havent tried using Moors or Egyptians against Mongols yet. Camel Gunners might do some sweet damage to them although their ammo doesnt last long.