I use dry tumbling the most using a vibrating tumbler, actually two. I keep the tumbler covered and dust is a non-issue. As the media ages,. I sometimes add a little polish and it binds up the dust. The media gets tossed when it does not clean any more. I have Berry Mfg and Dillon tumbles.
Sometimes, I wet tumble with stainless pins. It is usually when I am getting ready to make a large run of general shooting ammunition such as 38 Special wadcutters, 45 ACP 230 FMJ's or 9x19. While wet tumbling takes less time to complete, it requires more attention on my part. With an hour or so actual tumbling time, there is not much time to go off an do something else while the tumble is running. Then I fine separating the cases from the pins takes longer than it takes me to separate cases from dry media. I have a Thumler Tumbler and a Frankfort Arsenal tumbler.
Wet tumbling sure cleans and polishes the cases nicely.
When I first got into reloading, I used an ultrasonic cleaner to clean cases. I already had the ultrasonic cleaner in inventory. Back then, the magic case cleaning elixirs for use in ultrasonic cleaners were not available and I used soaps and detergents. Cases got clean but not shiny.
Drying cases after wet cleaning is a bit of another time consuming activity. Originally, I'd spread the cases on a towel and stir them periodically over several days. Now, I have a case dryer similar to the Hornady case dryer (
https://www.midwayusa.com/product/100809/hornady-case-and-parts-dryer). It still takes a while to dry the cases but at least I do not have to constantly attend to the cases until they are dry.
Various folks have various methods to accelerate the drying process.