The reasons why China has flatter business cycles than the US:
1. A major part of China economy is comprised of state-owned businesses / national enterprises with very large capacities and economic powers. Anything bad that happens to the economy can be immediately and silently negated without going public. Fluctuations are there, just not known to people.
2. In the sense of economy, people in the free world such as US believe in themselves whereas China people believe in the government that it will always do the right thing. Confidence in economy is as important as economy itself, especially in dire times. A group of people who believe no one but themselves would more likely become irrational and turn into chaos (economically).
3. US as the most developed country is more tolerant of business cycles than China who is still trying to make its stand. Therefore US has less intentions in flatting its business cycles, which makes it seem China has flatter ones.