Can you elaborate on this? I was of the impression that the Frankish heavy cavalry and its charge was not as widespread as you imply, and was completely absent on the Mongol side of the battles at Leignitz and Mohi in 1241.
Speaking of those, and thinking of a hypothetical Mongol vs English matchup, my money’s on the horde—if it weren’t for Ogadei’s death, I wager that more than just Poland and Hungary would have been massacred.
There was heavier calvary at those battles. Re:Liegnitz:
While the Mongol reserves of light calvary advanced to their positions on either flank, the vanguard, which had been a mangudai, broke and fled. As soon as the front and flank of Henry’s pursuing calvary came under the full fire of the Mongol archers, smoke bombs were let off from across their rear, screening them from the rest of the army, and once the Mongol heavy calvary had moved in for the final blow, the archers rode through the smokescreen and shot down the hapless infantry.
From Chambers.
It is almost certain that heavy calvary was at Mohi/Sajo river with the main Mongol army, they just weren’t singled out for particular mention. And the heavier calvary was definitely the arm of decision in the accounts that have come down from Kalka, when a heavily outnumbered Jebe Noyan and Subedei Bahadur broke the combined Russian/Cuman army in 1223.
But while there were heavier versions of Mongol calvary, I wouldn’t say they were necessarily the exact equivalent of feudal knights. Again, Chambers:
*The heavy calvary wore a coat of mail with a cuirass made of oxhide or iron scales covered in leather, and the light calvary wore either a cuirass of lacquered leather strips or else a quilted kalat and no armor at all. Next to his shirt every soldier was required to wear a long, loose undershirt made from raw silk…
In battle the heavy calvary replaced their traditional Mongol caps with iron helmets and some of the light calvary wore helmets made off leather…
…A lasso hung from his saddle and a dagger was strapped to the inside of his left forearm. Apart from these, the light calvaryman carried a scimitar and two or three javelins, and the heavy calvaryman carried a scimitar, a battle-axe or a mace, and a twelve-foot lance with a horsehair pennant and a hook below the blade.
The main body of the Mongol army advanced into battle in five single ranks, the first two of which were heavy calvary and the last three of light calvary. Well out on their flank and on either flank rode three seperate detachments of light calvary and one of these would be the first to engage the enemy. If any enemy took the initiative and attacked on a flank, the detachment of light calvary that engaged him would become the vanguard and while the main body wheeled to face him, the outriding detachments that found itself in the rear would gallop round to cover the exposed flank. Once the vanguard was engaged, the light calvary in the main body would advance through the ranks of the heavy calvary and gallop forward to join them. The light calvary did not usually engage the enemy at close quarters but rode across the front, showering the ranks with well-aimed arrows, or, if he was advancing, withdrew ahead of him and shot over their shoulders witrh equal accuracy. When they had opened his ranks and left them disorganized, they broke on to either flank, leaving the front clear for the heavy calvary to drive in the final blow. If the vanguard failed to create a gap, the light calvary on one of the flanks would be sent forward to attack the enemy’s flank at right angles and then, in a maneouvre that was known as the tulughma or ‘standard sweep’, the heavy calvary would gallop round behind them and make their charge in the rear of that flank.
But whenever possible the favourite tactic was the mangudai…*
…and so on ( I got tired of typing 
).
So the Mongols made use of a mixed calvary force, with heavier units equipped with lances and armor-piercing weaponry to drive home the attack. But while heavier than their comrades, they were probably still lighter calvary than, say, your average Teutonic knight of the same period.
That should be: …well out on their front and on either flank…
Thanks, Tamerlane. I was hoping against hope that you’d be by to help me out. 
I think that this dispute has been definitively resolved by Ms. Sinead O’Connor:
[crooning]
Nothing compares . . .
Nothing compares to yew
[/crooning – and ducks and runs away out of bowshot]
I think there’s a few misconceptions on the draw weights for both types of bow.
The english longbow had a draw weight of 80 to 120 lbs on AVERAGE. Specimens with even heavier pulls (150+ upto 200 lbs) have also been known to exist, but were rare.
Similarly, the bows in use by the mongols were of a pull weight of some 60 to 120 lbs with some rare specimens going above that.
As for whom would win in a battle between medieval european armies and the mongols, it depends on the commanders.
Mongols tended to do so well due to the genius of their military leaders. But eventually they were defeated by middle eastern armies in the middle ages. And that’s a close a comparison as you’re likely to get. European medieval armies fought and defeated and were defeated by middle eastern armies through out the crusades.
If you’re talking about fully armored knight of the late 13th and 14th centuries though, that’s a different story. You can’t compare light mail and leather to a full field plate harness.