Many competitive shooters do not like removing the carbon from the insides of the case necks. The say the carbon inside the case necks gives more uniform bullet release. They also do not like walnut tumbling media treated with any type polish that may end up in their barrels.
At the other end of the spectrum some competitive shooters who wet tumbling seat their bullets long and then re-seat the bullets just before a match to break any bond between the bullet and case neck.
I do not shoot in competition and much prefer wet tumbling with SS media. But I also remember just brushing the inside of my cases and using 0000 steel wool to clean the outsides of my cases.
Sometimes I think the saying "He who has the most toys wins" might be over rated and life was simpler when we didn't have all these new "toys".
I tumbled in the dry stuff for many years. Last year I decided to try the Sonic wet cleaning method. The set up for wet is more time consuming with measuring water and cleaner and warming up the solution but after I rinse the cases and run a cotton swab over the primer pockets they're much cleaner overall than the dry media method. Sometimes I do still use the dry media (corn cob or walnut shells - I prefer the corn cob because walnut shells leave a lot more dust) to finish the polishing. There isn't enough polishing compound in the media to migrate from case to the barrel so I don't get too excited about that stuff. Some guy I know uses steel wool to remove any hint of tarnish and then ends up with microscopic bits of steel wool in the ejector groove. Bujt he's happy because there's no polish residue on the case ... go figure. And no, tumbling in stainless media is not going to work harden your brass.
I have the same set up along with dry vibratory polishers and a cheap ultrasonic tank. The Rock tumbler does the best. I use one pound of media per cylinder with a half teaspoon of Lemi Shine and a squirt of Dawn detergent. I run around seventy five or eighty deprimed .223 brass at a time per cylinder. Add the items and then cover the contents with water, about half full. I believe the recommended max weight is three pounds. The lids need to be lubricated to assemble easier, don't want any leaks. Start the motor and then set the drums on and run for three hours. If you think less will do it by all means try it I just do three hours to be sure. A very useful gadget to have is a salad spinner, after separating the brass and rinsing throw them in there and spin the water out, just don't let the lid come off. I lay the brass on some dish drying mats I bought from Dollar Tree and suspend a heat lamp over them and in about fifteen minutes they are dry, you might roll them around a couple of times and a small fan helps. One of my reloading friends uses a dehydrator to dry his. Don't over do the Lemi Shine or they will be dull and once dry handle with gloves or they will tarnish. I still use the corn cob to clean up after trimming and de-burring.
I'm new to reloading and have the Frankfort vibratory tumbler. I've been using corn cob and a 1/2 tsp of the Frankfort polish. They come out looking about as new as used brass could look. I still have to clean the primer pockets and I run a quick brush down the necks.
I tried the Hornady Ultrasonic cleaner and it was just too much mess for me so I returned it.
Since I'm not shooting at 800-1000+ yards yet I'm not sure how much more OC cleaning is going to make a difference in my world but I suppose at a certain level any variable you can remove from the components and process will have an effect.
I bought a bag of walnut to try but I have read a lot about dust issues.
Walnut is dusty so I would advise against dumping the brass and walnut into the separator inside your house or reloading room. I run my tumblers out in my shop and when it's time to empty put on a dust mask and a pair of nitrile gloves to handle the brass. I will guarantee if you tumble de-primed brass with walnut you will get pieces stuck in the primer flash holes, it's alright if you are going to run them through the sizer just make sure the decapper is in place to clear the hole. I always use compressed air to blow the dust off and clear the holes. It's really not a bad idea to wear gloves the entire time you are handling the brass due to lead and who knows what else is on it. I got talked into cleaning several thousand pieces of brass one time and after sorting through about a thousand my hands were black, I have worn gloves ever since.
I decap, throw them in the ultrasonic, lay them on a towel to dry overnight, size, throw them in the tumbler in corn cobs to remove lube, then I clean out the flash holes, do a quality control check on the brass, check trim length, prime and load.