従事 is a noun. We use this word when we write resume. For example 販売業務に3年間 従事。 携わる is often used to introduce a person or myself. For example 4年間、日本語教育に携わっています。

どういたしまして！I hope this helped you in any way.

Thank you for taking your time in answering my question! I really appreciate it ^^

Wow, it's such a tough question. First of all, 従事 itself is a noun whereas 携わる is a verb. If you want to put 従事 into a verb, it will be 従事する. But this is only about a part of speech, if we compare the meanings I guess we could say they are pretty much the same. As I wasn't sure of it, I looked up both words in Japanese-Japanese dictionary and when I looked up 携わる, it said 従事する there but somehow not vice versa. So this will become my personal opinion, but I think people usually use 従事(する) for occupations or some sorts of lifework but 携わる could be used in smaller situations like being involved in a project, organizing an event, creating a book and so on. I apologize if I couldn't make the difference clear and thank you for asking a great question.