In general, a person is "concerned about" something or someone. A thing is "concerned with" something or someone. "I'm concerned about my friend. He's been acting strange recently." "I'm concerned about the upcoming test. I don't think I prepared enough." "The book is concerned with the impact of Prohibition on American culture in the 1920s." "The doctor's work is primarily concerned with eating disorders, but it also involves physical therapy."

For me they are the same and interchangeable. Perhaps the 'about' form is being a little less direct, or more general in the observation (their concern), but the difference is subtle and others may disagree.

Adding to Jason’s excellent examples, this might also help you: “concerned about” involves the human emotion of worry or empathy, while “concerned with” doesn’t have emotional content but simply means “related to” or “having to do with.”

I commented instead of answered and I moved my answer to the question answers, but now I don't see how to delete this comment... This message here is concerned with explaining its own existence.