How did the Mongol bow differ from the medieval English longbow?

Different tools for different jobs used differently by different people.

Remember, from a population base of about the same size (two million) the Mongols deployed far more archers much farther from home. There were twice as many Mongol archers (30,000) at Mohi alone (thousands of miles from home) than there were English archers at Crecy, Poitiers, and Agincourt (right next door) combined (15,000).

The English would not have done any better, nor worse, with the Mongol recurve bow. The Mongols would have done worse with the longbow. That’s due to how they fought with them, not how good or bad the bows were.

Draw weights were comparable. English longbows ranged from 80–120lbs at the beginning of the Hundred Years War (which the English lost BTW) to 100–140lbs by the end. By the 16th century most of the bows found on the the ship Mary Rose were in the 140–160lbs range, with the heaviest at about 185lbs.