I've done both, but the only thing I use my dry tumbler for now is to clean One Shot or the like off already primed brass. Not going to do that a lot, I'm persnickety about corncob stuck in the primer holes. May not matter, but I just have to tap, tap, tap to get it out.
So for me, it's the opposite of what a lot of folks are saying: dry tumbling is more high maintenance than wet. It helps that I don't bake or dehydrate brass, just let it air dry.
My equipment, in case anyone's interested: the original, big Franklin Arsenal wet tumbler, a 3 gallon bucket, a 1/4-inch gold-panning seive, a 5 gallon paint straining bag, salad spinner, disposable aluminum lasagna pans for drying, Armor All Wash N Wax, citric acid, pins, FA magnet. You can probably tell how I do it just from that, so I won't go any further.
The Wash N Wax does a good job of deterring tarnish on stored brass, better than just corncob alone, as you would figure. Not enough data to compare to NuFinish or similar in corncob.