Walnut cleans better/faster, but doesn't polish to as high a sheen.
Corncob polishes to a high luster, especially if you add a bit of Nu-finish, but won't take of heavy tarnish or soot.
I use the combo after matches, because the brass I bring home might not all be mine or if I'm out practicing and the previous user left a lot of brass laying on the ground...I especially like it when I follow a security companies qualification/training sessions.
I use straight corn cob to remove the lube (lanolin/alcohol) on my handgun cases