I've seen it both ways with brown bear, and it can be dumbfounding.Not my experiences with big bears but each had their own experiences. The big brownies have another level of tenacity unmatched by any hooved animal I’ve encountered. All thing being equal!
A bear that's sleeping, relaxed, and unaware of your presence? They will sometimes flop like a deflated balloon, provided the first bullet hit has substantial energy release and is well placed in the chest cavity.
A bear that's high strung, scared, mad (as in sow with itty bitty cubs, or a bear on a meat cache), or been wounded with a marginal shot(s)..., they can take a merciless pounding and keep on going (or coming).
Other brown bear hunters tell me they've also observed this when hunting and shooting brown bear. I think it boils down to adrenalin. After their adrenalin starts pumping, they're much tougher to stop. Their tenacity for life goes up proportional to their adrenalin concentration, IMO.