score:9
Only two large-scale battles between these two radically different types of cavalry occurred: Legnica and Mohi. Both of these battles resulted in extremely convincing Mongol victories, with the Mongols subsequently advancing at will across Poland, Bohemia, and the entire Danube Valley. Only the death of Ogedei Khan in December 1241, and the consequent requirement that Subedei's forces retire to support his claims at the kurultai, spared Europe from further ravishing.
The scale and completeness of both victories attests that the Mongol style of warfare was likely superior to anything in Europe until the late 18th century, its command and control systems orchestrating constant feints, withdrawals and ambushes that so exhausted every enemy that they became easy pickings for the final assault.
A critical key to understanding cavalry warfare is the recognition that each horse only has a small number of charges in him until he requires a lengthy respite for rest and feeding. The tremendous weight of a fully armoured European knight reduced both the length, and the number, of available charges significantly.
Both the Mongol cavalry itself, and their style of warfare, was intended to minimize this exhaustion for their own troops, and maximize it for their opponents. Once the European knights were hors du combat from exhaustion, the Mongols closed in for the kill against the immobile infantry, while harassing the knights just sufficiently to prevent them from recuperating.
The Mongol achieved this through the use of a small horse of great endurance, lightweight armour designed mostly for protection against arrows, and many scores of arrows for each of their mounted archers. An extensive command and control system of flags directed troop movements, and a sophisticated logistical network kept the archers continually supplied with fresh arrows without weighting them down.
No-one the Mongols fought, except themselves, could cope with this combination until their forces fragmented to a size that could be surrounded and overwhelmed by sheer numbers.
Update:
Note that the battles of Legnica and Mohi were fought with home field for the Europeans, in early spring (April 9 and 11, 1241) when all the disadvantage of fighting in the hot summer sun in full armour was negated. The campaign began with the forcing of the Verecke Pass in the Carpathians into the Hungarian Plain, about as unfriendly terrain for mounted steppe archers as one can find, and the utter destruction of the defenders under Denis Tomaj.
Upvote:2
Setting aside the purely military argument, I would like to underline the way political organization impacts the outcome of battle and war. In battle itself, European medieval armies were essentially fragmented and incoherent masses of warriors. There was no such thing as moving as a body or attacking as a body. Each warrior, very highly trained and equipped in himself, could not have been coerced by the commander to act in concert with his comrades. The commander did not have the authority to do so, given the fact that his soldiers were in themselves independent political entities, and did not have the means, because the capacity of tactical action is acquired through military drill and instruction. Only a standing army is capable of that, and the feudal system didn't know such thing. The French knights, for instance, were so fiery in their desire to clash with the enemy at Crecy, that they trampled under their horses the Genovese crossbowmen who began peppering some on the English side. The commander, once the enemy was in sight, had very little control over the army.
The Mongols did not have that. Theirs was a highly centralized political system, almost despotic in nature, and the military organization reflected that very well. The soldier was a mere tool in the hands of his commander. There is a huge difference between an army in which the commander has great difficulty in restraining his men from attacking or compelling them to do so and an army in which the commander has the right to put to death anyone who does not show unflinching obedience. The latter can act as a tactical body, the former cannot. The maneuvers the Mongols executed could not have been achieved without the highest degree of psychological unity and coherence, itself achieved by strict and regular military drills.
Again, I don't want to make the purely military aspects seem negligible, I only wanted to highlight this very important principle which fundamentally molded military history.
L.E. There is another very important aspect which the lack of discipline negatively affects: the capacity of employing tactical victories in order to secure a total, strategic victory. Back in the days of feudal warfare, once a battle was won, the losing side could easily pursue a policy of detente, retreating in a fortress, for instance. Besieging was very costly in terms of both tactical considerations (knights are incapable of disciplined conduct), logistical considerations (supplying an army with food in enemy territory) and political considerations (after 40 days of army service, the knight had the right to return to his fief). Therefore the war resulted in a white peace, or in a peace slightly disadvantageous to the losers. The Mongols, on the other hand, seemed to be very effective at both field and siege battles, the main reason for it being primarily their superior discipline and their ability to keep large armies together for a long period of time.