A rifle may allow you to make a shot you would have to pass up with a shotgun. One bear I shot was on top of a rock outcrop, at a steep angle above me, and about 150 yards out. Given those conditions, the .308 is easily the best choice of your 3 options. As it was I got the deed done with a .303 loaded with 180s, but any .30 caliber cartridge from the .300 Savage to the .30/06 would have produced similar results if loaded with a similar bullet. Of course the cartridge the rifle is chambered for is only part of the question, the rifle itself must be suitable for this type of hunting. If your rifle is a 12 pound target rifle with a 26" barrel, topped with a 12X scope, there might be better options. But a .308 carbine that weighs between 6 and 8 pounds, and is topped with a small fixed power or a low power variable scope is almost perfect IMHO.
At one time I would have turned my nose up at the 7.62X39, but if you loaded one with a quality 130-150 gr bullet (read TSX/TTSX or the like), that can make 2200 or so, and is used within the effective range of your particular rifle, it would put a hide on your floor.
The short barrel 12 ga repeating shotgun has a fine reputation as a personal defense bear gun. But while self defense and hunting may appear to be similar on the surface of it, there are differences other than the reason to shoot. The primary difference is the range at which you may have the opportunity to shoot from, another is the level of accuracy that is required to make a shot at a partially obscured target. Either of these circumstances can cost you a shot if you're hunting with a slug gun rather than a rifle, but neither would come up in the self defense scenario. Of course the style of hunting you choose has an impact on your choice of gun as well, and from a stand or a blind over bait for example, a 12 ga would do as well as any rifle. While some of the black bears I've seen in the bush have been in thick cover, the vast majority have been along cut lines, power lines, railway tracks, across slews, or on lake shores, suggesting that even in a country where heavy cover is common, a longish shot is possible.