I remember reading a Jack O'Conner article many years ago where he said he shot a grizzly at moderate distance and watched his 30-06 180 gr. bullet blow right thru it and plow into a gravel bar right behind it, I think the bear dropped dead in his tracks.
There used to be a guide up on the Bonnet Plume that used a .308 on a few Grizzlies with no complaints.
I think you have to be accurate first, and calibre won't matter much, with the caveat that you use a stout enuff bullet.
Hell you hear these stories all the time about Eskimo's using all sorts of light calibres .222's to 6 mm's on snow bears!
In short I have no doubt that a 30-06 loaded with 200 gr. premium bullet will get the job done at close range IF you put it in his vitals.

458:
You, sir, are a class act in my book and I too appreciate your postings. Thanks for coming on the board and expressing your opinions and relating your experiences. Bear in Fairbanks