If you've hunted much with a side by side or O/U shotgun on upland birds, I doubt very seriously that you would like carrying and shooting them with a Drilling.

At close ranges normally associated with bear defense, a 12 bore loaded with solid slugs (not Foster) or round balls will give you MUCH more power and stopping potential than any small bore rifle - including a .375.

There is NO factory slug available that I would trust for protection from grizzly attack. For that purpose, a solid round ball or bullet as in Ed Huble's "Alliant Steel" 12 bore loads would be my choice - from a rifled barrel. For that purpose, I picked up a pound of Alliant Steel" yesterday. A 12 bore rifle, properly loaded and sighted is a fearsome weapon indeed and is not relegated to bear-spray ranges. Indeed, it is a powerful hunting rifle should be sighted for that purpose.

You want bullet stability for straight line penetration and a smooth bore shotgun may not give that straight penetration. The rifled bore will probably give poor performance with shot - so is only for bullets or round balls for defense and/or hunting.