As the saying goes, "any port in a storm."
But if one was choosing a firearm specifically for grizzly defense (and let's not even debate how (un)likely that is), neither a .308 Win or a 12 gauge is what I would want in my hands. Nothing you can throw out of a shotgun is really designed to hold together and penetrate large, tough critters -- let's face it, buckshot/slugs are designed for lighter big game. Again, if that's all you have, that's what you use -- but not what you choose.
Can a .308 Win drop a grizzly humanely in a hunting situation? Sure it can, although it wouldn't be my first choice by any means. But a charge situation is very, very different. You have a fast moving, very angry bear hopped up on adrenaline, with the very signficant problem of having a poor shooting angle in that the bear is facing straight on. Your only means of stopping the bear RFN is to either break down critical bone and/or disrupt the CNS. Either way, you want a bullet that's going to penetrate hard and deep, and break through anything it finds in its path. This is not the time to shot soft lead balls at a sloped skull against which they'll want to flatten and/or deflect.
I found it interesting on the one grizzly hunt I did that the guide carried a .416 Rem Mag, which seemed overkill even on a charge. After lengthy discussions in camp, backed up with some actual hunt footage he shared with me in his home, I now quite appreciate the very different scenarios of hunting a bear and stopping one. He didn't carry that .416 trying to look cool or make a ballistics point to anyone -- he carried it as the best solution to what (for him) is a very real problem. As he put it, "I don't care what anyone thinks about my rifle. I just care about going home to my wife and kids after every hunt." Unlike just about all of us, he *has* had to shoot a few grizzlies and brown bears in ugly situations (in this case, add "wounded" to the list of negatives above), and he has learned through experience that you simply cannot hit an angry grizzly too hard.
In retrospect, I think his choice of firearm shows a lot of careful thought -- a 5 lb Ultralight Arms bolt action carbine with a ghost ring peep sight. Yes, it kicks like the Devil himself (being a Gunnut, I just has to shoot it

), but it's light and handy enough that he carried it absolutely everywhere -- that rifle was NEVER out of reach. For what he needed it for, it was the right tool.
Well, that's my 2 1/2 cents...