In Dan Carlin’s Wrath of the Khans podcast, he characterises the difference between the Chinese and European military forces during the time of Genghis Khan similarly to the major and minor leagues of baseball, with the Mongols fighting in Europe being like a major league team playing in the minor leagues, and the Chinese military being like the major leagues. Was this true of the Chinese military at this time, and if it was true, at what point did it stop being true? This question was inspired by both the aforementioned podcast, and also the letter written by the Qianlong Emperor to George III, the tone of which strikes me as interesting given (my personal and probably wrong conception of) British military supremacy at that time.
When you say the military power of China in the 13th century, which China are you referring to?
At the beginning the 13th century, most of China was ruled by the Song Dynasty. Now, "China" then was smaller than today's PRC, but it was still massive, something like 2 million square miles, with a population somewhere between 50 and 100 million people. That's similar to the population of the entirety of Europe at the time. You can't say "how did it compare to similar armies in Europe" because there were no similar armies. There were simply no states comparable in population to Song Dynasty China.
Of course, the 13th century is a time of massive change in China, because of the Mongol invasion. By the middle of the century, the Mongols had conquered half of China, and by the end they'd conquered the whole thing. So that meant that China was more militarised, with more soldiers. Of course, it was split in half, but even the Northern Yuan Dynasty and Southern Song each dwarfed any European state in population. The biggest European state (the HRE) only had a population of about 5-10 million at the time.
I know a bit about the decline in Chinese military power at the end of the Ming dynasty, and then the decline of Qing military power in the 19th century, but I'll let someone else who can give more details answer that. I will say though, that under George III, Britain was in no way one of the world's pre-eminent powers. Look at this map: at the time of the letter, Britain controlled just the orange bits on that map. http://www.bbc.co.uk/staticarchive/5d08832e8bedf0e9cf28cc9a35ecb2e019edefe5.gif Britain was an up-and-coming power, whose technology gave it an edge in the wars in India, but it was pretty small compared to many other powers (and had actually just lost more than half its settled territory to rebels). The amount of people ruled by Britain was tiny, compared to the Qing Emperor. As your link mentions though, this was to dramatically change by the middle of the 19th century, as the industrial revolution and control over India boosted Britain's power projection into the East, military technology, number of troops, and money to invest in the military.
