Rifle or Handgun? I'm assuming you're talking about stalking the bear versus a surprise the other way around.
More ft-lbs of energy is one possible guide: .50 BMG, 45-70, .416, any of the Nitro's over .450, Weatherby .460 Mag and Weatherby .458 Win, even the .338 Lapua has some pretty good qualities for a stand-off.
Reach-out-and-touch the bear at a standoff distance would also bring in some higher velocity / smaller calibers, but I'd leave it to the guys who have actually taken game at close range for anything any smaller, not wanting to hack off the bear and switch the roles.
In the pistol arena, there are some very serious cartridges .44 Mag and up, particularly the .500 / .577 / .600 / .700 rounds that have significant energy. (I would be interested in hearing from anyone who has intentionally taken a grizzly with a 9mm Glock.
Many others would feel comfortable with a .300 Win or .308.
Heck, there are some that can probably consistently drop the big bears with a .243, God bless them.