Understand up front. I wouldn't be going handgun hunting for Kodiak bear on Kodiak, nor for big browns anywhere. I would carry a handgun as protection with complete confidence though, but wouldn't use it unless it were mandatory. My reason is that I can put a rifle bullet precisely where I want it a lot quicker, and on a fast moving target. With a handgun I want the target moving slow or stationary, or if for defense use, close enough that the powder blast burns hair.
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I was a bit salty with that reply, which was not a proper answer, but a personal opinion about what I would or wouldn't like.
I have many mold customers who have killed brown bears with handgun bullets from my molds, mostly using revolvers of 44 and 45 caliber, and all have reported quick kills. Key to success, or quick killing power is to use a load that produces the ideal DV, or Displacement Velocity, per my kill formula, which is around 125, with 130 absolute max. !00 is excellent but requires a bit more precision shot placement through the vitals to kill rapidly enough to prevent damage from close in shots, damage to the shooter that is. This power level or better stated, wounding potential can be attained with a host of cartridges and firearm types.
Here is the displacement velocity formula: Multiply meplate diameter in thousandths by velocity and divide by 4. Use this formula only for non expanding flat nosed bullets. I find the easiest way to use the formula is to divide the meplat diameter by 4 and punch the result into the memory on a small calculator. Now multiply that answer by several velocities till a velocity is found that produces the desired DV.
Animals up to moose, huge brown bear and bison are incapacitated instantly when hit through the chest with a DV of 125 to 130, and either fold in their tracks or are able to move slowly for only a few feet. If any of my readers have questions about this. Throw them at me. The formula has stood without being argued since I introduced it in 1989. I have received thousands of testimonials to it's accuracy and not one report of it being wrong.
Be forwarned. DON't go over thinking more is better. The numbers above are optimum, and going higher will slow kill speed.