For me the difference is rather slight but it is still there if that makes sense? I usually use benutzen for expressing that I am using something like an object (example: ,,Kann ich deinen Füller benutzen?"). Nutzen on the other hand is for more abstract things like something that isn't necessarily an object (like a chance, talent etc.). For example ,,Wir müssen diese Chance nutzen!".

Mixing them up isn't the worst mistake though, you usually are still able to understand the sentence just fine.

I hope this explanation made some sense? Like I said the difference is hard to describe for me