I would NOT use either Scotchbrite synthetic pads OR stainless steel pads in a good gun barrel.
Both WILL damage the bore.
Scotchbrite synthetic abrasive pads are just that....ABRASIVE, just like sand paper.
Using it will quickly destroy the bore.
Stainless steel scouring pads will scratch the bore, even if it's slightly softer than the barrel. Barrels are not all that hard, and I don't recommend using ANY stainless steel brushes or other cleaning material in the bore.
Either use cleaning materials specifically made for guns, or use COPPER Chore-Boy pads for lead removal.
Using any of these to clean a barrel shot with jacketed bullets is totally unnecessary, since they will have little effect on copper bullet fouling.
You need to be VERY wary of using any non-gun specific "expedient" cleaning material or chemicals.
These will often damage an expensive gun barrel, and the people who tell you it's OK to use them will NOT be standing by to buy you a new gun if it ruins it.
Over the years I've seen a good many examples of guns damaged or ruined by using non-gun cleaning gear, and the people who did the damage never offered a good reason for using the stuff other than they could save a few pennies.
This really is a matter of "Penny wise, Dollar foolish".
Bottom line: Continue using the stainless steel scrubbing material and you WILL ruin the bore, sooner rather than later.
For ordinary bore cleaning use standard BRONZE bore brushes, solvent, and patches.
Do not use stainless steel bore brushes (Those are for gunsmith use in bores so badly neglected you have nothing to lose) and do not use over-sized brushes in bores.
Brushes wear out quickly, and solvents eat them just like it dissolves copper fouling. Buy your brushes in bulk.
If you shoot lead bullets, either buy a Lewis Lead Remover kit, OR you can use the COPPER Chore-Buy pads.
DO NOT attempt to "Blow the lead out" by shooting jacketed bullets.
All this does is "iron" lead into the bore making it that much harder to get out, and the barrel can corrode UNDER the lead.
Worse, attempt to shot the lead out of a bore with just a little too much lead, and you'll blow a ring or bulge in the barrel.