- The Chinese and American people are both great people.
- The Chinese and American peoples are both great peoples.
Which kind of wording is good?
People when meaning the population of a country or nation is a countable noun, thus:
people noun [ C ]
All the men, women, and children who live in a particular country, or who have the same culture or language:
The French are known as a food-loving people.
a society:
Customs similar to this one are found among many peoples of the world.