Not wanting to start anything here, but I will share my personnel experience. I have used both tumbling and ultra sonic cleaning on muzzle brakes. The tumbling dulled the finish on one of my brakes.
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I tried ultra sonic cleaning with dawn, simple green and other gun cleaning solutions. They did work, but took many hours in the sonic cleaner. It would take an entire weekend to clean my suppressor. So now the controversy. After reading a thread on this site I decided to try CLR. It worked great on the muzzle brakes and the suppressor.
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Do be cautious in the use of CLR. It works well. Some members have seen some evidence of etching on SS barrels. I have not used CLR on a barrel yet. After removing the muzzle brakes and suppressor from the ultra sonic cleaning I rinsed them with water and brake cleaner then blew them dry with compressed air. The ability for CLR to remove carbon I think is shown pretty clearly in the photos above but use with caution.