I wouldn't skip carrying the gun. It seems that if a bear is really hungry, bear spray won't stop them. Famous bear researcher Vitaly Nikolayenko was found with an emptied can of bear spray next to his half eaten body.
It's basically the same risk either way. But bear spray seems like it is a
generally well-proven deterrent, if used correctly. And I say that while still having personal doubts...if you spray a bear at a distance, it seems like you may just be needlessly antagonizing him. Up close, I wonder if his instinct to eliminate the threat would override any pain he may feel from a direct hit to the face. Kinda depends on if that stuff really incapacitates or just serves to deter from a 'you're not gonna like this' POV.
With humans, quality OC or CS should negate the threat pretty well...firsthand experience with a military CS chamber showed me how well that stuff immediately cuts off my breathing and renders my eyes useless.
I'd lean toward preferring a center mass magdump with a decent pistol round and hoping like hell it hits a vital organ. People definitely say a big, thick, flat bear skull is a poor choice to shoot at. If I was worried about bears, I'd definitely be packing something with some oomph...10mm or .40 seems like a good choice for an auto....this is where you really get into, uh...'armchair bear hunter.' A lot of failures to drop bears seem to be with high-powered revolver rounds, which seem like a worse alternatire. .44mag or larger seems good on paper, but 5-6 shots of something hard to control seem like an interior choice to 10+ rounds of mag-dumpable .40. Same can be extended to long guns...yeah, a .308, .30-06, .338...those will do some damage, but will you even get more than 1-2 rounds off?