Took me a while, but i realized that this is a resurrected thread from 6 weeks ago. Pretty sure that Antique guy, is not going to answer.
I would like a follow up from the OP to see how he made out with his 308 and Black Bears. I ate a lot of moose meat growing up shot by my father and his 60 year old Savage 99 308. No big game animal in north America is wearing kevlar. The question is not whether a 308 will kill game, its at what range, how quickly, and how capable it is in a more dangerous situation. A large angry Bear at close range for instance.
If the question shifts from the use of the .308 as a bear hunting cartridge to the use of the .308 as a bear protection cartridge, the only significant change that one needs to consider is his point of aim. In hunting the most important criteria is to kill the game animal as quickly and humanely as possible. In the protection and defense scenario the most important criteria is stopping the bear's forward progression, the idea being that if the bear can't touch you he can't hurt you.
A chest shot is an excellent choice for the bear hunter, as no bear hard hit through the lungs will last long, but the chest shot is a poor one when the requirement is an instant stop, and there are all sorts of reports from people who have hit bears with rifle fire multiple times in the chest, only to have the bear finally drop at their feet . . . or not. One really interesting aspect of this is that the power of the cartridge in question seemed to have little bearing on the outcome, whereas shot placement made a tremendous difference. So if not in the chest, what is the correct aiming point in a dangerous bear scenario? Well it depends. Where is the bear relative to you, on higher ground, lower, or level? Is he approaching head on or quartering? Are you his target or is someone else? Is contact imminent?
A CNS shot is the surest stopper, but requires a cool hand, as simply shooting a bear in the head is the wrong answer. A bear's brain is a small target tucked away in a massive head. The brain pan is only the width of the snout, and is shallow, located behind the eyes and ahead of the ears. Additionally, the head might well be in motion from side to side, although often a bear committed to an attack will be focused intently upon his prey, and his head is motionless. At close range, the scope sight might confuse the shooter who forgets that his bullet is a couple of inches below his reticle. About now we will start hearing the old saw about bullets bouncing off bear skulls, when in fact the guy on the gun shot a might high, and the bullet cut a furrow across the bear's scalp. If the bear was about to make contact with another person, or was actually on another person, the shot you need to make should be as far from the victim as possible, watching the shot angle to avoid hitting him. A shot through the rear hips will break the bear's transmission and pretty much anchor him in place, but it won't be pretty. It might be enough to cause the bear to roll off his victim, if that was the scenario. Once the bear's forward progression is halted, the rifleman can change his position to make a safe killing shot.
If I was to select .308 ammo specifically for defensive use against bears, I might choose a stronger and heavier bullet, than the one I might choose for general big game hunting, with a balance towards penetration rather than expansion. Defensive shooting suggests very close range, feet rather than yards. This is where the bullet's velocity will be highest, and where the chances for cup and core bullet failure to occur are the greatest, particularly considering heavy dense bones in particular are targeted, rather than ribs and soft tissue. For this reason I would probably opt for a 180 gr TSX. The heavy bullet weight moderates the muzzle velocity, and the bullet is known to penetrate well, due to it's modest 1.5X expansion. Having said that, I do recall making a particularly spectacular black bear kill at close range with a .303 loaded with factory Remington 180 gr Corelokts, so don't consider yourself poorly armed with a .308 and say Federal 180 gr blue box ammo.