Disclaimer: I have only tried the mirena, not the copper coil.
I was tempted by the copper coil because of it being hormone free but one of the common side effects of the copper coil is that it can make your periods heavier and I already have issues with that so didn't want to risk them getting worse!
Other than that, I don't remember the nurse discussing any other potential issues with it. But I went to the family planning clinic here and they do a pre-fitting appointment where they go through it all with you and work out which one is best so I'd recommend that!