If you set out to prove that China generates more CO2 than America, then you do so by ignoring the populations of the countries. The percapita numbers have zero relevance to this calculation.

If on the other hand, you wish to prove that the average Chinaman is responsible for as much CO2 as your average medieval peasant, while your average American is responsible for as much CO2 as your average medieval lord (taking into consideration all taxes and lands), then population numbers are critical. (Note that the simile was not chosen for accuracy but for effect. And I made no effort to look at actual numbers. Further that I would be astonished to find it accurate. However I would also be astonished to find that it did not give a roughly accurate view of the ratio between Chinese and American percapita CO2 generation.)

[Forgive the stilted prose - I am drawing to the end of Stephenson's Baroque Cycle, and it is eating my brain.]