Which one is more commonly used in Chinese speaking communities: 年轻 or 年青?
Both 年轻 and 年青 mean "young".

However, 年青 refers to adolescents. It's about the people at this stage. 

年轻 means young; it means people who are between the ages of 10-20. but 年轻 can also be used to compare the ages; For example, person A aged 50 is younger than person B, who is at the age of 60. Even though people who are 50 and 60 are not young, but in comparison, 50 is younger than 60. You can only use 年轻 in this case.

If someone looks young, you also use 年轻 instead of 年青.