I use ultrasonic only because I happened to have one. A decade ago I was rebuilding an engine as a hobby project and bought one of those huge units off eBay.
It works well but I don't like it, and if I get more into reloading enough to justify it, I'm definitely going to get a dry tumbler. Three reasons based on my experience with ultrasonic:
1. They take longer, in my unscientific, completely non-data-driven anecdotal opinion. It could be my cheap unit, but if I was going to fix it with a more expensive one, why not switch to a tumbler anyway?
2. You can't see what's going on as easily. Mine is a large 30L unit and it's nice because I know I can clean basically anything. But once that cleaning fluid gets even a little murky, it's a total swamp in there. To check the progress you have to dip in and pull out a case or two. Not a huge deal, but I feel like with tumblers something's always floating around the surface where you can get a glimpse.
3. You never know what to do with the dirty cleaning agents. Some are water-soluble, but they don't clean as well and I just don't feel right dumping them down the drain. Auto shops won't take it like they do with oil, they're hard to recycle at home (filter), and who wants to make a special dump trip with jugs to drop off in the hazmat? I could be just totally wrong on this, but I feel like the walnut shell litter is friendlier to dispose of and you do get a lot of use out of it...