I use both.
I used to use only brass and didn't know much about copper fouling. When I started reading this site I switched to copper solvent and a nylon brush and was getting a lot of copper out so I figured I was also getting carbon.
Then I decided to use one of my brass brushes from a new rifle cleaning kit I had purchased and was surprised on how much carbon I had missed with my previous cleanings.
Now I use 4 swipes of a brass brush with rubbing alcohol, then a patch.
Next I use 4 swipes of a nylon brush to apply the solvent, then a patch.
Then I use the alcohol on the nylon brush to get the solvent off, (2 swipes,) then 4 swipes with the brass brush and alcohol, then a patch.
Then I use oil on the brass brush to get the rest of the carbon, (which really gets a lot more carbon than anything I've tried yet.)
I finish off with an oiled patch.
That is with my new rifle and it seems to be getting all the fouling and carbon. I have broken the barrel in that rifle, with my older rifles I will use more swipes since they foul a lot more... Except my Winchester 30-30, which doesn't really copper foul all that much; I use only oil on the brass brush, then every 10 outings I'll use copper solvent.
I leave my barrels and chambers oiled just in case I failed to remove all the solvent, I run a dry patch down my barrel and in the chamber to remove the oil before shooting.
I don't know if alcohol is the best thing to use, I just started using it in place of a carbon solvent when i ran out and it seems to work as well as anything I had used previously.