Were there any objective historical accounts as to how the Yuan army fought? Why were the Southern Song able to deal with the Jin army, while they unable to deal with the Yuan army, and why were the Europeans able to get a handle on the Mongols after Mohi while the Chinese were unable to adjust? Were Chinese fortifications weaker than European fortifications, since European stone castles were impregnable to Mongol siege engines while the Chinese forts like Xianyang fell easily with counterweight trebuches?
When the Mongols attacked Europe, that was very far away, and to improve mobility, I suspect Mongols may have left their heavier siege equipment behind. China was a lot closer to Mongolia.
But the Mongols did have trouble with fortifications. Much of their success against well fortified cities and forts came as a result of either treachery, as in the case Baghdad, or because people surrendered the forts or cities voluntarily as part of Mongol propoganda. When the Mongols did eventually conquer the Song, their army contained a lot of Chinese, who no doubt provided the expertise in capturing fortified places.
However, the Chinese may also had less experience at the time with fortifications. For most of its history it was a unified country, and its enemies, like the Mongols, were not really into building fortifications. So they didn't get involved in extensive sieges like people farther west, where you had a lot more political entities that were more or less at equal levels of technology, and a lot more fortifications. So while the Chinese had the basic technology for sieges against fortifications, they just had as a rule less practice in engaging in sieges and capturing fortifications. So it is not surprising if their siege equipment, as in the case of the counterweight trebuchets, was less advance. Their fortification at the time seems less sopnisticated too, I don't see the concentric layers of defense you find in European or Japanese castles.
In addition, you hear a lot of accounts of a city falling in China because someone opened the gates. China has a history where the Chinese often helped some foreigners take over because they sometimes thought that foreign rulers would be preferable, for example in the case of the Manchu, who had a lot of help from Chinese in conquering China. That kind of history didn't exist in Europe.