I've always found copper fouling harder to remove than lead. It's harder, resists scrubbing, and ammonia-based solutions only remove the top layer of it.
Lead, being softer, I've found easier to remove.
One of the best lead removers is Iosso Bore Cleaner, which is a slightly abrasive cream that comes in a tube. Hard to find, but Midway has it at a reasonable $5 or thereabouts. One tube lasts longer than expected.
I work the Iosso Bore Cleaner into a patch, then use a patch jag that will hold the patch tight in the bore. Work this back and forth until it feels too easy to be doing any good. Push the patch out and you'll likely see long threads of lead on the patch, where it was once deposited in the grooves.
For .38/9mm handguns, I use a 5/16th length of dowel and tap the patch through with the dowel (it's a tight fit, so you won't be able to move it by hand).
For the .44 or .45 I use a 7/16th length of dowel.
The flat-faced dowel ensures the patch fits tightly. When it's tight, it grips the lead in the grooves and lands and pushes it out. The wooden dowel eliminates any chance of bore damage.
For revolver chambers, I use a slightly oversized bronze brush (.40 for .38/.357 and .50 for .44 or .45) attached to a short length of cleaning rod. Chuck the cleaning rod into a cordless drill, dip the brush in Hoppes No. 9 or your favorite solvent, and run the brush in and out of each chamber at low speed.
No need to run fast, low to medium speed worked forth and back will get the lead out of the shoulder in the chamber.
And if not, use the dowel and tight patch method with Iosso Bore Cleaner. A tight patch tapped through will push it out.
One warning, though: use a copper or bronze brush, not stainless steel. A steel brush may damage or slightly enlarge your chamber. The bronze or copper brush, being much softer than cylinder steel, doesn't pose that danger.
Oh, and the Iosso Bore Cleaner is wonderful for the bores of cap and ball revolvers and muzzleloading rifles. It will smooth them wonderfully, after they've been thoroughly cleaned. It will also remove any black powder fouling you may have missed.
For cleaning shotgun barrels, it's great. Removes rust, plastic, lead and any other crud.
And no, I don't get a commission from Iosso! I should though ... I've been promoting it for years. It's that good.