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Now part of discrepancies in calculations is that different groups- CIA, World Bank, IMF use different methodologies.
There are sources showing China bigger and they use PPP, personal purchasing power. which takes account of the total buying power within the country from the total income. Part of that is that services are so much cheaper and in things like haircuts the Chinese in total can buy more haircuts than the US, although per capita they are still much less as the US is well ahead per capita.
Other sources, like the IMF cited above, look at exchange rates and that is where China falls well short and reflects there ability to purchase things like oil, coal, steel on the world market and more reflects their geopolitical power.
This is detailed in the Guardian piece here
THe Guardian looks at this definition in measurement. and notes:
"The obvious solution is to use the contemporaneous exchange rate: multiply China’s yuan-measured GDP by the dollar-per-yuan exchange rate, so that it is expressed in dollars. Viewed in these terms, the US economy ($19.519tn) is still more than 50% larger than China’s ($12.144tn), according to the latest figures.
By contrast, measuring GDP in PPP terms is more appropriate for comparing standards of living because it accounts for the fact that many goods and services are cheaper in China than they are in the US. Generally speaking, one yuan spent in China will go much further than one yuan spent abroad. While some internationally traded goods have similar prices, things like haircuts – a service that cannot readily be exported or imported – are cheaper in China than in the US.
The PPP measure has many uses but assessing geopolitical power is not one of them. It is not helpful in answering the primary question that most commentators fixate on: how China’s economic size and power compare with the US’s in the broader contest for global supremacy.
For that, a more relevant consideration is, for example, how much money China can contribute to the International Monetary Fund and other multilateral agencies, and how much voting power it should get in return."