Some will say that ammonia contained in Brasso will weaken brass.
A spoonful of Brasso in a load of media and cases doesn't have enough ammonia to damage the cases. Lots of people have used Brasso in their media without ill effects. Many other types of metal polish or wax will also work well: Flitz, Peek, Autosol, Nu Finish, etc. If the brass isn't coming out shiny, try tumbling for 24 hours.
I much prefer wet tumbling due to cleanliness. Dry media can get the outside shiny-looking, but it still has a film on it that turns your fingers black when you handle the cases. You also don't have to worry about dust and stray pins are much easier to pick up than particles of walnut shell or corncob.