I know they use slug and buckshot loaded 12 gauge's in Alaska and other parts for defense from bears...would think either would work fine with slugs at close range..say over baits..but a center fire in the .270 or 30/06 range and up would be my prference...even black bears can be tough, and a lot of people loose bears after hitting them, especially in the fall when they are fattened up...so the bigger the better in my opinion for bears..something that anchors them, and afford the occasional bad shot that happens in the real woods...

Even a 410 with #6 bird shot in the face works pretty good, kinda like sticking its face in a bee hive and blinding the bear! I would take the 12 over the 16 any day. But having something is better than nothing!

Truly a well placed shot with either of them with a slug should work.

I say, get the biggest slug you can get!, but my dad and I always say, "never hunt anything that if you don't shoot it, it can kill you". There is some very good advice.

Both will kill a bear just fine at close range and with good shot placement.

O.K note to self/others.
NO HUNTING WITH MR. Cooper in "bear country" !
As to your question. I worked in a taxidermy studio for awhile and had the chance to talk with several "bear guides" about this. They ALL said "the BEST bear gun is a 12ga. with slugs".
I would thing that a 16ga. would come close though.
My uncle took a Colo. State Record Black Bear with a bow too.

A 12 gauge slug packs plenty of swat at a close range. I wouldn't shoot at long distances with a shotgun though.