Near as I can figure, I've been using JB Paste for close to 40 years. It was standard among all competitors in my benchrest competition days, and if there's anyone persnickety about bore care and wear, it's those guys.
But in my experience it's at its best when fouling (whether copper or lead) is pretty minimal. Kind of a regular maintenance process rather than a curative. If you let fouling build up much, you're going to go through a whole bunch of JB before patches come clean.
I've cleaned my share of bad lead and copper fouling out of guns, and for my money it's hard to beat some of the solvents and procedures intended for the purpose. I've heard good things about the electical doohickies for the job too, but never tried them.
For severe leading, as I've encountered in cartridge revolvers firing soft lead bullets that are moving too fast, there's a little deivice called a Lewis Lead Remover. You can get them from Brownell's, but to my knowledge they aren't set up for rifles. Basically they pull a rubber bore-sized plug covered with a brass mesh like window screen through the bore. It will scrub lead like nobody's business while not damaging the bore.