What comparison are you looking for? This is a very broad question.
Perhaps the biggest difference between these two countries in my opinion (as an American) is the fact that people in the US have lots of personal freedoms and those in China do not. The suppression of speech and religion in China is very different than what we have here.
At the moment, another major difference is that China's economy is booming and ours is not. Of course, they are growing from a low base while we are staying relativley stable starting at a high base. But they are definitely an up and coming economy while we are not.
There are some similarities between United States of America (USA) and Peoples Republic of China (PRC). But essentially these are two very different kind of countries. The similarities between the two countries are in terms of large geographical area and very high GDP. But there are many differences in political, and cultural nature of the two countries.
While USA represent the best of the capitalist form of economy and government with very high levels of personal freedom, PRC represents the most successful case of communist form of economy and government in which personal freedom is highly restricted. Also in spite of very high GDP of PRC, it lags behind USA considerable because of its very high population.
Culturally china represents one of the oldest culture in the world. In comparison, USA is comparatively a very new nations with no old cultural roots. Also people of USA come from a wide range of ethnic background. In comparison, population of PRC represent more homogeneous ethnic background.
Currently PRC economy is developing much faster than that of USA. However the PRC economy is dominated by labour intensive economic activities and is still very much dependent on exports to developed countries. In comparison USA economy is dominated by technology and capital intensive activities and domestic consumption.