Most of these answers are correct and part of the bigger picture. In 2005 the population of Europe was estimated at 728 million, China is estimated at 1.36 billion.
Europe is 4,010,000 square miles China is 3,600,947.03 square miles. Which makes the fairly approximate in size and arable land is fairly approximate as well. If you factor in European descendants as well you get:
USA :300,000,000
Canada: 30,000,000
NZ: 4,000,000
AUS: 20,000,000
Plus a handful of others whicha re harder to clear up ie Brazilians, South Africans, etc... but add those up and you have 354,000,000 + 728,000,000 = 1,082,000,000. Really there's more but difficult to follow. So pretty comparable.
Further if you only include "Han" Chinese and minus people of Mongolian, Muslim, Tibetan, Miao, Manchu, Hakka and all the others minority descent, you can can cut China's numbers down, but they're all Asians and all in one country now so probably shouldn't.
It's really the world that is over populated, watch a movie called "The 11th Hour" were all in it together, but China in particular has always believed itself to be the centre of the Earth and thought there was no reason to explore, plus the Himalayas, deserts and oceans that buffered China made travel to anywhere good difficult if not impossible in the early days although they did populate Japan, what is currently North and South Korea and some believe North American Natives are Chinese descendants also.
Also, most of the Chinese population live where they do (along the east coast) because of favourable growing conditions that were able to support a higher population throughout history. They estimate at least 60 million people already lived in the area in 0 A.D.
And finally, in more recent times (1950's to 70's) Mao pressured people into commune's to procreate and they were crawling on each other like a big box of hamsters for years. Mao wanted to have enough people to win a nuclear war, but that war never happened and it caused another significant population increase.
http://en.wikipedia.org/wiki/Demography_of_Europe