How come the mongols had a hard time taking European Stone Fortresses but not ones in China that were made out of stone?

I'll start this with a caveat: my knowledge of medieval warfare is almost entirely limited to England and France, so someone with more knowledge and experience on the Mongols will undoubtedly provide a better answer. I nonetheless have a couple of books, namely Timothy May's The Mongol Art of War and Chris Peer's Genghis Khan and the Mongol War Machine, which look at how the Mongols fought and have information that I'll use to propose two complementary answers: that the Mongols did have a hard time taking Chinese fortifications, and that the nature of the European campaigns made siege warfare unwise.

The first thing to do is to put the Chinese campaigns in perspective: the war against the Jin Dynasty lasted almost 25 years and the war against the Song Dynasty lasted almost 40 years. The Jin Dynasty initially intended to use a combination of superior numbers and existing fortifications against the Mongols, but multiple defections by allies and client horse nomads saw their best pasture land cut off from them by the Mongols. Subsequently, the war became all about fortified cities, which the Mongols had to reduce one by one.

The Song Dynasty was protected by good natural defenses in the form of mountains between them and the Mongols and, though the Mongols did attempt to outflank them, they were able to hold off for quite some time and win several battles. Eventually the twin cities of Xiangyang and Fancheng were besieged, and these held out for six years, until supplies ran out and the newly introduced counterweight trebuchet made considerable impact on the walls. With the fall of the twin cities, the Han River, and from it the Yangtze River, was now unprotected from the Mongols and they could strike wherever they wanted in Song China.

What does this have to do with the European campaigns? Well, the important thing to note is that, after the initial 1241/1242 campaign, Mongol actions in Central Europe were almost entirely large scale raids, not actual invasions. Against raids, with a lack of time for circumvallations or heavy siege equipment, stone fortifications worked very well. Unless taken by surprise , they were difficult to damage with the equipment the Mongols would have had with them, thus making an assault a costly proposition.