“The claim that the United States has more coronavirus deaths than China is false,” Senator Ben Sasse, a Nebraska Republican, said in a statement after Bloomberg News published its report. “Without commenting on any classified information, this much is painfully obvious: The Chinese Communist Party has lied, is lying, and will continue to lie about coronavirus to protect the regime.”
A couple points:
In Hubei (maybe everywhere?) China didn't count in their official tallies people who tested positive and were asymptomatic. Partly because 1) the tests they used were not very accurate, so they relied on confirming positive test results with pulmonary scans, basically checking for pneumonia. Asymptomatic folks weren't double-checked that way, but just told to isolate.
2) Due to a major outbreak, China went with a pretty strict mandatory lockdown in Wuhan and Hubei. So they weren't really concerned who was positive or not, since they had a province-wide quarantine. Instead, they focused on who had symptoms, were presumably contagious and needed treatment. 3) Supposedly China ran out of test kits in Hubei at some point, though that was never confirmed.
China said this week they would release the figures on asymptomatic cases that tested positive. Whether they will do so and if those number will double the test-positive cases in China is unclear. This is most likely what Sasse is grousing about.
The official case numbers for every country reflect the level and availability of testing, and the quality of the test used.
No one believes the number of test-confirmed cases = the actual number of infected. It's a proxy and mostly a sign of how many people had symptoms and sought testing/treatment. Quicker, more reliable and widespread testing, which is becoming more available, will of course uncover more infected people.
China, like almost every country, didn't take the virus seriously or take early action until there was a significant and dangerous outbreak. But China did take measures to contain and limit the spread after things got bad. These were effective and provided a pretty good model on what works.