For example, Shanghai is a "highly-populated city " or "one of most populous cities"in China. Are they both correct? If so, which one is more common?
This is just like many and most.
Definition of many by Google:
a large number of.
Definition of most by Google:
greatest in amount or degree.
"highly-populated city" means a city that is populous while "most populous city" means the city is more populated than any other cities.
The difference is that most is a superlative while highly populated is like a normal adjective.
Here are few more examples:
I have many games.
I have the most games in the world.