You left one out. Stainless Steel media tumbling. There are all kinds of Pro/Con lists out on the net. Here are some things to think about. Dry tumbling is cheap, reasonably effective on most dirt, and has worked for a long time. It does tend to produce dust, and there can be bad things in that dust. The wet methods have been known to produce "shinier" brass for folks (whatever that means to you), get the inside of the case cleaner, and keep the dust/particulates contained.
SS tumbling has a pretty high intro cost, but the media is basically indestructible. So it pays off in the long run somewhere. It does add one somewhat significant extra step to the process, namely drying. After vibrating or tumbling with wet media/solution, you must dry the brass completely prior to any further reloading operation. Maybe a big step, maybe not.
Now, all that said, I still dry tumble with corn or walnut, and sometimes a little brass polish. Mostly because I have been doing it this way for a long time and it works, but I am really getting sick of the dust. I am seriously thinking of moving to SS wet. The results that I have seen are really compelling if you can afford the upfront, and don't mind the extra step of drying.
-Paul