Have always just used water, maybe some over-the-counter black powder solvent (e.g. often wipe bore with Hoppes BP solvent/lube when done shooting, before actual cleaning), but after reading this I thought I would try a brush, in my .36.
Have been using Grafs BP, which I must say is leaving a heavy residue in flash pan, and breach scraper is coming out with a good bit of crud. Anyways, on last couple cleanings, after a set and soak, breach scrape, and wet patches until "clean", I went ahead and took a few strokes with a brass borebrush, followed by another wet patch. Wow, was surprised how much black streaking I was getting after the patches were coming clean. Maybe my cleaning patches are just not tight enough on jag to get down into the very corners of the square cut rifling and the brush was getting that stuff out?
Will probably start using a bore brush routinely, right after the initial soak, just to be sure all crud is loose to swab out. Have used bore brushes my whole life on cartridge guns and I am in the camp that lifetimes of brass brush stroking will not affect steel bore.