Both methods will work just fine. I sometimes use the steel wool- 0000 only, on a jag or smaller brush - or - i use several copper strands of a Kurly Kate kitchen scrubber wrapped into a brush. This seems to work even better than steel wool, and even works as well on leaded rifle bores - without any damage whatsoever. This is what I use in my BP CTG guns.
: I rarely lead a shot barrel now, as I use plastic wads that hold the ball centered.
: Dry paper is good as it 'grabs' the lead. I merely find less work is involved with steel wool or the Kurly Kate scrubber strands.
: I use a bore solvent with the wool or copper wires.
: Something else that works extremely well is the lead-remover cloth - the yellow ones. They are sort-of black magic - kinda scary how that works.
: I've used the lead sovents with mixed results. Used with steel wool, of course, it's great.
: I have used nylon-strand re-inforced paper towel as patches and that works well. Some equipment and comercial cleaning supply outfits have it.
; As I use cotton diaper or flanel sheet material along with too-thin BP rifle patch material for cleaning, I don't use paper very often, although it works just fine.