The correct answer to this open question is the following.
The argument that evaluates the extent to which levels of centralization in China and European states differed in this period is the following.
Although you forgot to include the period, we can say is from 1200 to 1450.
This was a period of changes in Europe. The continent was in the process of leaving the Dark Ages of the Medieval Times, to enter into the Renaissance period that started in Italy, approximately in 1300.
In Europe, the Feudal society dominated most of the European territories But from 1200 to 1450, local powers started to end due to the power of dominion of strong monarchies that conquered territories to amaze more power and control over new lands. This was a period were big and strong kingdoms were formed. The authority of the king was unquestionable. The king established power and control over its territories and people had no rights. All the decisions were made the ling itself.
In the case of China, the Emperor in that time established a bureaucratic system where only the best and most prepared elements could be members of it. Historians say that there were difficult tests for people trying to be part of this autocratic government. It was a time of economic growth in China, where the Yellow River and the Yangtze River were used to promote trade and transportation of people and merchants. Gunpowder represented a great product to trade and the Silk Road increased trade in the region.