The mongols adopted the best tools of their enemies, they had a complete army that included siege weapons built by chinese siege engineers. They were the first to use artillery in Europe. They conquered far larger and better fortified chinese cities than any piddling castles in Europe.

And you can't trap the mongols, their mobile army lived off the land and moved far too fast with a lethality that european armies couldn't deal with.

The death of Chenggis Khan was the only thing that saved Europe from a massacre and enslavement by the mongols.