I have done both, but have settled on using a vibratory bowl with corncob and polishing agent (cerium oxide).
The bowl cleans the brass and brings it to an high polish. The inside is also cleaned, but not as well. I leave the primers in for this operation, to keep medium from clogging the primer hole. I've never found enough residue in the primer pocket to bother about.
Ultrasonic cleaning is very thorough, inside and out. You must deprime prior to cleaning, to minimize air pockets. The brass is left somewhat dull, and will stain badly if left in the tank overnight due to extraction of zinc. Cases must be thoroughly rinsed and dried before proceeding. The best method I've found is putting them in a mesh washing bag and hanging the bag in front of a floor fan overnight.
Tumbling the cases in a bowl afterwards will also dry them, at some risk of having clumps of medium lodged inside. Chemically clean cases tend to stick on the expander/funnel of my Dillon 550B.