The Germanic barbarians didn't supposedly want to mess up the political system, but they still wound up doing so.
There was less of a gap in regards to population size and what the Germans could natively produce when the Western Empire fell though. Everything that could be produced in Rome could be produced by the German lands.
The Mongolians, on the other hand, lived in a land that was not suitable to produce most of the goods produced in China, and the population gap was much wider.
The Germans were closer to being an economic equal to Rome than the Nomads to China's north. Also, the invaders of China were unified enough to keep China in one piece, the Germans were not.
So it would seem to me that the thing that kept China stable during the conquests was the large discrepancy between the native economies of conquer and conquered, and the fact that the conquerers had a different mindset towards China than conquers in other parts of the world.
One could say that the conquers weren't just after material wealth, they were actually after the concept of China itself. The Germans were at the end of the day going after the wealth of Rome, and they only had a passing interest in the concept of Rome. When the Ottomans conquered the eastern half of the empire the leaders liked the concept of Rome, but the common Turk still viewed themselves as a Turk. When the Nomads who conquered China did so, the commoners among their ethnic groups started to view themselves as part of China, and not China as part of them.
What regions of the world do you think a similar mindset could develop?