As with most topics everyone has an opinion, and mine is that if you are in an area where dangerous bears might be an issue, then you should carry a gun designed specifically for that job. That does not mean that you need to go the custom route, but in terms of shotguns a 12 gauge repeater has become standard. Of those, the type made for fighting with rifle sights, swivel studs, short barrels and long magazines and perhaps a side saddle seems to be the best suited for this particular problem.
A 12 gauge also offers the best selection of ammunition. When it comes to ammunition for use against bears, carry and practice with the best slugs you can find. Brenneke slugs have a very good reputation on game larger than deer. Of the foster style slugs that I have tested, Federals have the highest velocity, but Brenneke's penetration is superior.
In a pinch, any gun is better than no gun, and your 16 gauge duck gun will probably save the day, However, if you intend to be in a place where you have a reasonable expectation that you might have to kill a bear in self defence, the purchase of one of these guns, many of which cost between $500.00 and $1000.00, is cheap insurance. Whichever gun you choose, practice is what will determine the outcome if you need to shoot.
Edited to add - We have discovered around here that when an individual who has never been in a "shoot for your life" situation before, short stroking a pump shotgun is a real concern. The use of a well maintained quality semi-auto seems to resolve this problem.
