Tumbler?. Not for me. So far I'm "handwashing" my cases but an ultrasonic is on the way,
I'm with Sam1911 on washing.
When I got into reloading many moons ago, I washed cases in n ultrasonic cleaner because it was what I had in inventory at the time and could not afford a tumbler (by the way, Amway LOC did a great job. I don't know if they still market it though).
I let cases dry for a week to make sure all the moisture was out of the case.
I guess you could accelerate the process by using an oven but that was not the way to win friends and influences wives in my household.
Dry tumbling is the way to go. Quick, easy and cases can be used immediately after they are removed from the tumbler. I run media until it absolutely does not clean any more. I probably change it once every couple years or so shooting 5000 plus rounds a year. The media would probably last longer if I would shut the tumbler off after a couple hours but I let it run all night. Pretty cheap cleaning.
I do wet clean with stainless pins once in a blue moon when the spirit moves me but again, it takes a while for the case to dry. I wet tumble when I have a ton of cases that I want to look pretty.
Does it make my rounds more accurate--no except that it makes me feel better about them. Do not discount the psych factor.