I like Hoppe's No. 9 when I am cleaning around sensitive areas, such as plastic or wood. And, I do prefer to use it when cleaning the barrel with patches.
That said, when it comes to metal (stainless/blued steel, or aluminum) surfaces, I do like using brake cleaner. It does an excellent job of removing dirt and carbon fouling, as well as oil and grease. And, being that it's in a pressurized spray can, it works well to "blow" dirt out of the hard to reach places.
Generally speaking though, I spray the brake cleaner on a Q-tip and use it that way. This way, I don't have to worry about it getting all over the place, or affecting any surfaces that I don't want it on. Plus, it's a bit safer.
I have never had a problem with brake cleaner permanently affecting the finish of a stainless, blued, or aluminum firearm. And, I have used it on the inside of chrome-lined barrels with seemingly no negative effect. That's just my experience. Your mileage may vary.
As posted in my thoughts on using bore snakes, I especially like to spray a small amount of brake cleaner (you don't need much) on a bore snake, ahead of the sewn-in bristles. This does a good job of helping to break down the "gunk" in the barrel. And, since the brake cleaner evaporates fairly quickly, it's easy to clean the bore snake without much waiting time (I used hand soap and warm water).
I know this is a Mini-14 thread, so I won't dwell long on this...but one of my biggest uses for brake cleaner is when I clean my AR-15's. In short, anyone who has cleaned an AR knows they can be a witch to clean. But, the brake cleaner helps to "blow" the fouling out of the chamber lugs. And, it makes for quick work of the bolt carrier group and inside of the upper receiver too.
OK...there's a few of the 'pros'. Let's get into the 'cons'.
You do have to be careful about getting brake cleaner on non-metallic surfaces. I've never had a major whoopsie, but I have noticed that it will affect painted surfaces negatively. So, if you have a painted surface, I would use something else (e.g. Hoppe's No. 9).
Brake cleaner will strip the metal of all dirt and grime. This is good in that it cleans the metal. However, you need to make sure that you re-lube and/or protect that area again, in order to reduce friction and/or prevent rust. Not a big deal, as you should be doing that anyway. But, it's a point worth making.
The smell! Yes, brake cleaner has quite a strong smell. Be sure you are using it in a well-ventilated area.
Also, WEAR safety glasses. Since the spray can is under pressure and the brake cleaner will shoot out of the can at a high rate, there is a potential for it to hit a crevasse, or nook and cranny, and come back and hit you in the eye (ask me how I know...). It burns pretty badly. In fact, this is why I like to use Q-tips most of the time.
Anyway, just use your head, and be sure to keep the brake cleaner away from sensitive finishes/surfaces, and you should be fine.
OK...that's my two cents.
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