Here I go again:
My personal ideology on this one is to shoot the heaviest 12 gauge slug and buckshot (you could even alternate rounds) rounds that I can fire accurately and fast. For me that is usually max-loaded 2 3/4", 1.25 ounce slugs, sometimes with 00 buck. Plus I get a bonus round for going shorter. I don't think the bear would notice too much of a difference in that quarter-inch.
For me, being competent with the shotgun is way more important than using 3" magnum ammo. If the gun kicks so bad it scares you when you look at it, then you will never practice enough with it. Semi-autos like the Remington 1100 kick less as well, mind you they can be heavier to carry and might not be as reliable as a pump.
I watched a man nail 5 targets in 1.3 seconds with a Beretta 1200 semi auto. I asked if I could try, and took 3.8 seconds to do the same. Keep in mind that this is under controlled conditions at a range and we were prepared for the targets. Still it shows that practice means a lot.
I practiced modestly with my Winchester pump and was able to nail 5 targets in a bit less than four seconds too. I operated that gun instinctively because I used it for all my hunting as a kid, but I sold it and bought a Remington. Now I have to train not to reach in the wrong spot for the safety (slide release too). At one point, a bear could set a place, pour a glass of chardonnay, tuck in a napkin and stick a fork in me before I got that gun to go off. I still wonder if I will go into 'Winchester mode' under stress. I haven't practiced with it or handled it enough.
Dry fire practice is important for bringing the arm to bear

and snapping off that first quick shot. I bought a set of fake shotshells called 'snap caps' and ran them through my Winchester a jillion times. It helped make the handling the gun become second nature. If you had to recognize a threat, unsling and fire 3 times accurately, how long would that take?
In those adrenaline-pumped, split-seconds between when a bear charges and you decide whether or not to shoot, the most important thing is to have a gun that you handle and aim instinctively. You have to be both fast and accurate. That means practicing with it so much that it becomes a given where the muzzle is pointed. If it kicks the crap out of you inside of ten rounds, then I would consider another reasonable loading, or something else.
I concur that AK rounds might not be enough. FMJ's don't transmit shock well, and hollow points are likely too frangible. If a Nosler partition soft point type of bullet is available, then that may be a good option. If you are the fastest most accurate AK shooter in your state and can find suitably-constructed bullets, then that is the gun you should use. Same would go for a cowboy action shooter and his lever-action .44 magnum. If it handles like part of your own body and is powerful enough, then use it.
I still like my 12 gauge; I get .338 Win Mag power at close range in a much faster shooting, lighter weight and more compact package. I don't have the option of a .44 magnum handgun, but I am not very good with one anyway. I stick a Sidesaddle on my Remington for extra rounds, and I have the option of flares, rubber bullets and bird shot for other safety and survival applications. Ever shot a duck with an AK?
Hope this helps,
Phil