When I started tumbling cases I did so due to the volumes of pistol brass I was loading. With carbide dies I wanted them as clean and shiney as possible. IF fo no other reason they looked great.
I got tired of dumping it out every two weeks or so and having to pay 8-10 bucks for replacement media, so did a little calling around. I found that I could get 50# of either for about 18 bucks at most, from a local sand blasting supply. Well who needs 50# of media much less 50 of each. I got hold my my shooting buds and we split it up and ended up with a major supply for little of nothing.
I tried either by it's self, as well as several mixes of the two. I also added in several different recommended polishes as well during all of this. My final outcome was a mix of 2 parts corncob to one part walnut with about 1/2 teaspoon of Flitz put in and mixed up well, before adding the cases.
This combination will flat out knock the crud off of and out of 2-300 or so cases in around an hour. I don't think it does the insides of bottle necked cases as well but it still gets a lot of it. I also generally polish them up for about half an hour in plain cob and flitz after sizing just to get any lube or whatever minute burs around the necks off.
For the Flitz, I use the tumbler bowl as a measure for the media, and figureing it 2/3 full of media - 1/2 teaspoon of Flitz. I suppose this could be anything really but it has worked well for me. I put in the fresh media, turn on the tumbler, and add the Flitz slowly to try and avoid any major clumping. Once it is in, let it run for about 15 or so minutes initially before adding the cases. This helps to dissapate the major clomps, and keeps the clumps from settling into a case.
Hope this helps.