What does the population data on cities suggest about the place of cities in early world history versus modern world history? Can you explain why the Han Empire and the Qing Empire had much larger armies than the Roman and British empires?
The thing that clearly jumps out about the size of cities in the empires of 2000 years ago compared to those of more modern times is that the modern cities are so much bigger. What this should tell us is that cities are much more central to modern economies than they were 2000 years ago.
The reason for this is trade, which comes about because of technology. 2000 years ago, technology was still relatively primitive. This included agricultural technology. Because agricultural technology was not advanced, farmers could not really grow enough to feed large numbers of people. This cut down on the potential size of cities as a larger percentage of people had to engage in farming. This also cut down on the number of people who could be artisans or who could engage in trade. Artisans and traders also tend to live in cities, so this, too, reduced the potential size of cities.
In modern times, technology has boomed (even 100 years ago). This has freed people from having to farm because farmers could produce more with fewer workers. It has also increased the amount of trade that is possible as manufacturing technology has made it possible to create more goods to buy and sell. All of this manufacturing and trading tended to happen in cities, making cities more important in the 20th century than around the start of the Common Era.
As for the question about army sizes, you need to look at the army sizes in comparison to land mass and to population. The two Chinese empires were 2 to 4 times larger in land area than the two European empires. They had more than seven times the population of the European empires. This would have meant that they would have needed much larger armies to keep the peace internally and to protect against outside invaders.