Copper will have a smaller o.d. than c.i. or PVC. I would seek out the right coupler.
It's not the copper end that is in question. It is the CI end. CI O.D. for 3" pipe size is 3.8 inches or larger depending on class. PVC O.D. is 3.5" This suggest that the coupling would be a bit large for the PVC but it was tight. I had a hard time getting it on.