I like my Dewey rods, but they are the only "high end" cleaning rods that I have ever owned. On my .22 cal stuff, I have taken to using the "O.T.I.S." kit that I bought for my AR.
As far as the chemicals, I have never used Bore Shine, so I can't give any input there. As long as its not a copper solvent, the bronze brushes should work just fine. Nylon always seemed a little wimpy for me.