Great question! To add to Su.Ki's excellent answer--and, as she says, "Chinese" is more common. It seems to me that--with China and with the name of other countries-- I use "China's" when I am personalizing China, thinking of it as an actor that is doing things. "China's decision to make huge investments in railroads and other infrastructure turned out to be a wise one." I use "Chinese" when I am thinking of it an adjective, when I'm thinking of "Chinese" as an attribute or characteristic. "This vase is red." "That vase is Chinese." "This is a heavy book." "That is a Chinese book." In many case it's possible to say it either way. "China's economy has been booming." "The Chinese economy has been booming."

'China's' is a genitive form, meaning 'of China.' 'Chinese' refers more to the nationality, language and the culture of China. For example, you would say 'I saw a beautiful Chinese painting in the art gallery'. But you might see the phrase 'China's trade surplus' in an article about the world economy. This has nothing to do with nationality or culture, it is simply 'the trade surplus of China' - just a figure relating to the country. In most cases, we would use 'Chinese', for example 'This is a beautiful Chinese silk scarf'.

China is a country, Chinese are people have citizenship of China :)