There are a number of calibers that can be employed in a pistol that can raise your odds of stopping a charging bear. You have specified two of them.
Most people have absolutely no idea what is required to stop a savage 35 mph, 250-350 (average) pound collection of claws and teeth found in a Grizzley. In the end bullet configuration within either caliber is as important as the bore itself. Ben Forkin, the bullet designer and maker for those interested in securing the roughest, toughest most appropriate bullets for their big bore pistol reloads has some very good advice. As the man that people like Bowen and others rely on for their bullets, we probably should listen. Large flat frontal surfaces ranging in the 450 grain arena appears to be the ticket. Penetration yes, sure, of course..but it is high SLAM factor that stops mass that large from moving forward without interuption. In fact, the best you can hope for is to make the beast vear before collapsing. By the way, the person's hand that pulls the trigger on Forkins LBT LFN 450 series will experience the same effect as catching an 8 pound base ball bat in their bare hand (in Bowen Alpine Ruger). The attacker will hate it..and the defender will too. But as I am sure the next poster will point out...its better than the alternative.
Your answer is the .500 Magnum. Why? Its about bullet mass, configuration and velocity. In the question raised, mass appears to be the bottom line.
Beside, all too soon this Old/New cartridge will be drawn into the next round of gun related legislation. Quickly, now, before the laws change again.