Steel brush is too hard for the barrel and it can ruin the rifling which could shorten the barrel life (& accuracy.)
I personally use a bronze brush in my handguns (never in my rifles) when there is a fouling. Most of the time, I use patches soaked with Remington bore cleaner. It leaves my bore very clean and very shiny.
Though I have never used it, I heard lots of positive comments about 'bore snake.' It's quick and easy to use. HTH.
The problem with steel breushes is that they will leave scratches in both the bore and chamber. Yes, they will get the fouling out but leave you with a bigger problem.
The bronze or nylon brushes soaked in bore cleaner have worked for me. Just remember to leave a fine coating of CLP in the barrel if you plan on storing it.
I concur with the replies on barrel damage by the steel brushes.
I use bronze brushes if the situation calls for it, and that's only when the barrel has lead or copper fouling. There are solvents designed to soften lead and copper fouling that can be used along with the bronze brushes, but I found that a bronze brush in good condition does the job all by itself.
I still have part of a bottle of PRO-SHOT PRODUCTS Lead and Powder Bore Solvent left. I get better results with it the longer I leave it in the barrel. I soak a patch in the solvent, run it through the barrel to completely soak the fouling, then leave it for a while. I've never left it longer than 8 hours before swabbing the bore out.
Results are a bit disappointing, but it can be done with a bit of patience and time. With lead fouling that came with 150 rounds of lead (cast) bullets, it took me three applications, and there was still a little fouling left.
I found that firing a dozen or so round of FMJ hardball after a session with cast bullets cleans out a lot of fouling. After that, a couple of passes with a bronze brush followed by a few patches with good 'ol Number 9 solvent, and the bore is clean, shiny, and ready for anything.
If I shoot only jacketed projectiles, all I need is the Number 9 and a few patches. No brush needed.