Brass and bronze jags and brushes are a no-no with copper cleaners, that's for sure. Be sure you rinse off the copper cleaner from these or it will attack them. I have used a slightly undersized nylon brush to drive a soft cotton patch through my bores when they were really fouled, and these did a pretty good job.

One bore cleaner that does an pretty good job on both copper and nitro foulding is plain old Birchwood Casey Bore Scrubber. This stuff surprised me. I actually removed some copper from one of my barrels after I got clean patches with Shooter's Choice Copper Remover.

Hoppe's is great stuff, but it just doesn't dissolve copper.