I submit to you the if you hit the skull of an elephant with a 12ga slug, it will stop. Ol' Karamojo was hitting the eye socket and other various holes in the skull. This is usually the goal even with the big magnums, though they do have the power to penetrate.
I won't say that a 12ga CAN'T do it, but I don't think so on a regular basis.
Say, just how many elephant was the OP planning on hunting with the 12ga or .308?