について・を巡って: the difference
についてN3
Meaning
Concerning, About, Regarding
Past papers
Tested 4 times in past papers
Example
この問題について、誰かに話しましたか。
Have you talked to anyone about this problem?
を巡ってN2
Meaning
Concerning, In regard to, About,
Past papers
Example
珍しい金魚を巡って、愛好家たちの間で激しい争奪戦が起きた。
A fierce battle broke out among enthusiasts over a rare goldfish.
How to tell them apart
「について／に関して」: neutral 'about'.
「をめぐって」: always involves several sides in disagreement, dispute or a fight over interests.