After experimenting with several kinds of media and both rotary and vibratory machines, I have settled on a vibratory tumbler and 24 grit walnut shell media. The key ingredient being the fine 24 grit media.
This is not the cheapest or fastest way to clean but, I like clean primer pockets and the 24 grit is fine enough to get in there and clean them without packing up anywhere and stopping things up. It just pours right out when you are done. It helps that I got what is probably a lifetime supply when Harbor Freight put 25 lb. boxes of it on sale for about $10.
If you are wanting it to clean primer pockets don't expect miracles though. It will get the main crud out reasonably quickly and that is all I really care about. But, if you want the pockets to be shiny bright.... well, I don't know how long you may have to vibrate them. Probably, TOO long.