Copper plated jackets are not as thick as full metal jackets. FMJ's are made by deep drawing the copper/brass into a cup, and then installing a lead core, and then swaging the bullet into shape. Very rugged.
The copper plating, while a thick layer of copper, isn't as durable as a FMJ.
Most copper plated bullet manufacturers advise against having the plated bullet exceed a certain velocity (1200 fps). There's no such restriction on FMJ's.
If you're talking about shooting a pistol at 50 yards+, then yes, you might see some differences. If you're shooting at closer ranges, any reloads will be more accurate than the ability of most shooters to shoot them.
So, for plinking, copper plated are fine. When it's important, use the FMJ's.