Commonalities I see. (Reflecting both how the US is now, and how I could see it evolving on its current path.):
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Mass surveillance with access to careers and positions of power dependent on living and thinking according to the party line. Wrongthink on social media results in real world consequence. (See political criticism in general in China, the reactions to the killing of Charlie Kirk in the US.)
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Mass tracking of citizens. Every movement of every citizen is tracked and recorded 24/7. Every action they take with a computer of any kind is recorded. Every corner of every city is monitoring 24/7 by camera networks and surveillance drones. All these records are constantly trawled by AI for patterns of dissent. The invasive surveillance state the Uyghurs are subject to is the future our leaders want for all of us.)
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Heavy police intervention in everyday life. (Checkpoints and showing your papers is the norm. Heavy integration between national and local law enforcement. Local law enforcement co-opted for political enforcement. Compare how China requires visiting foreigners to regularly check in at local police stations to the American ICE.)
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Economic system consisting of market economies with heavy state intervention in key national industries. (Both are taking outright ownership stakes in companies in certain key sectors.)
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Massive military spending for a military used to project power beyond national borders. (US more like Iraq or Iran wars. China more getting into wars you could call either revanchist or expansionist depending on how charitable you're feeling. Think Taiwan or some of China's land border disputes. Though admittedly the US is currently the far more interventionist of the two. But at the very least, both still maintain massive military-industrial complexes as major pieces of their national economies. China either has or will soon have the world's largest navy. They currently want to use it to take Taiwan, but when you build a tool like that, an expeditionary Navy has all sorts of uses as a tool of national policy. Once you're paying for the world's largest Navy, the leadership of that Navy will constantly be pitching uses for it. No Navy admiral wants to see the size of the Navy cut. It will always be tempting to deal with a meddlesome trade dispute by dropping some bombs on people far away.)
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Leadership chosen by performative but ultimately rigged and pointless elections.
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One party political control. (Communist Party, Republican Party.)
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The top leader is surrounded by a cult of personality. (Not sure to what extent Xi has done this. My impression is a lot less than Mao, but a lot more than other recent Chinese leaders. The Trump personality cult is more obvious. But at the least, both countries now have a clear precedent of the top leaders using cults of personality to maintain power.)
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Nonexistent or co-opted labor unions
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Birth rates maintained through state coercion. (I am not aware of any punitive measures implemented by China to raise birth rates. In the US, this looks like banning abortion and birth control. I think China is currently taking the carrot rather than the stick approach, but China has a clear precedent of using overwhelming state power to forcibly control the birth rate. See the One Child Policy. If they could justify that to lower the birth rate, coercive methods to raise the birth rate are also likely. Maybe tie access to careers to having children.)
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Lead by a group of leaders seeking to cement permanent control through mass automation and artificial intelligence.
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Close personal connections between the corporate and government leadership class. Through the Chinese lens, it looks like party members owning the big companies. Through the American lens, it looks like billionaire presidents and cabinet secretaries. The Venn diagram of the corporate leadership class and the government leadership class is a circle.
The US and China really seem to be converging to the same form of government. I suppose as both countries are heavily influenced by a class of billionaires with more loyalty to each other than to their respective nations, this shouldn't be a surprise. There's a reason Trump cozies up to dictators. These people are all copying each other's homework.
On paper, China will remain nominally Communist and the US nominally capitalist. But both are converging towards what is probably better called techno-fascism.