Black bear are not much harder to kill then a large deer. Grizzlies are a totally different animal. A large (not trophy) black bear will go about 350 pounds and a large (not trophy) grizzly will go about 650 to 700.
Now you'd think the grizzly would be 2X harder to put down.
Well,------ grizzlies are a lot more then 2X more bear, and for what reason I can't really say.
We have LOTS of grizzlies here in Wyoming. I have been around them for years and have seen first hand what they can do.
I used to kill black bears easily with various "deer rifles" and about anything that you can depend on to break a big deer bone will do on blackies.
Grizzlies.....well you want to use anything up to and including a 458, as long as you can shoot it WELL, and do it pretty fast.
Now I would galdly shoot a large Grizzly with my 270 as long as I could shoot without the bear knowing I was there. All animals on earth can be killed with small calibers IF you get to choose the placement and are willing to go home without shooting at all unless you get the shot you want.
Most of us don't want to go home without a shot. So it's best to shoot something "big enough" or even a bit bigger then you need, as long as you can shoot it WELL!
I am 100% certain you are better off with a 30-06 and 220 grain bullets, facing a grizzly then you are with anything more powerful, if you shoot the 06 well and you don't shoot the _____ < (add your caliber here) well.
You MUST shoot well!
If you have to face a bear that is mad, the rules are going to change, and not in a way you will like.
If you can hit an orange at close range in 1 1/2 seconds EVERY time, and your bullet will hold together and penetrate making a good sized wound, then you are fine with what ever you carry.
If you can't hit the orange EVERY time with more power, then the more powerful rifle is not going to help you against a grizzly, and in fact, it's likely to make things worse (if you can get worse then being killed......I don't know...)