What to rely on, while killing a grizzly
You rely on your skill, and your nerve. And afterwards, you rely on a good lawyer! Because the only way you are going to get off without going to court is if the grizz is chawing on you or a close personal friend.
you may eventually beat the charge, someone did just recently, but excpect to be in court for killing a griz.
As far as I know, there's still no hunting grizzly allowed in the continental US, and I don't think it is in Alsaka, either. Big browns, on the other hand are both dangerous, and game in Ak, I believe.
Any rifle of moderate power can kill griz (defensive), if you are capable of shooting it well, at speed, under extreme stress, and a medium rifle you can shoot well is better than a heavy one you can't.
The biggest grizzly taken in the continental US was taken with a .30-40 Krag. Big guns are comforting mentally, and certainly will do the job, but YOU still have to put the bullet in the right place. .30 caliber or larger, a repeater, iron sights, or low power optics (dot or scope), and your grace under pressure is what will make the difference, because you can't shoot griz until he (or more likely She) is a clear an present danger, and by the time that happens, they are going to be pretty close, and likely moving at speed.
One thing you don't want is to find your .338 Mag (or whatever) with its variable scope set on 9x when that bear is 20yds away!
Ammo with bullets suitable for penetration over expansion is a good idea as well. Bad idea to shoot a big bear with varmint bullets! You need somthing that will go through bone, and keep going. Expansion is nice when you are hunting, and can pick your shots. When shooting defensively, you have to take the shot(s) you get, not the ones you want.
There's a reason African dangerous game rifles are big bores and shoot solids. Its because under the most dangerous conditions, they work. Big bears aren't quite the same as water buffalo or elephant, but many of the same principles apply.
A 12ga with slugs (the sabot slugs are really impressive) is far from the worst choice for defense, against most anything.