They're both empires of more people than most human beings can hold in their heads as anything but an abstract concept, and the needs of an empire that oversees the welfare and fate of so many people actually tend to converge: they need energy. They need things for people to do. They need relative internal peace to preserve their territorial and legal cohesion.
And both China and the US go to great lengths to achieve their respective paxes, in different directions; China clamps down hard on information flow, the US launches aggressive extraterritorial military campaigns to "fight them over there so we don't have to fight them over here." China's surveillance state and incarceration polices may be more overt, but the Snowden leaks revealed the massive extent of passive surveillance of its own citizens the US engages in. China has its problems with "undesired" minorities; the US has a citizen-condoned police state of immense scope and violence... it imprisons more people per-capita than any other country, and has had several high-profile instances of police and "citizens watch" murdering innocent citizens who looked like they were in the wrong place at the wrong time.
And both China and the US go to great lengths to achieve their respective paxes, in different directions; China clamps down hard on information flow, the US launches aggressive extraterritorial military campaigns to "fight them over there so we don't have to fight them over here." China's surveillance state and incarceration polices may be more overt, but the Snowden leaks revealed the massive extent of passive surveillance of its own citizens the US engages in. China has its problems with "undesired" minorities; the US has a citizen-condoned police state of immense scope and violence... it imprisons more people per-capita than any other country, and has had several high-profile instances of police and "citizens watch" murdering innocent citizens who looked like they were in the wrong place at the wrong time.