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While a 223/5.56 will run laps around a slug on pure velocity - energy is what gets the job done. energy is a combination of mass and velocity (velocity squared times bullet weight in grains divided by 450,240 = ft lbs energy)

For large animals such as bears, it takes significant mass to penetrate hide, flesh and bone to a sufficient depth to actually stop the animal. A 556 will quickly shed velocity and not reach a vital (without exceptional shot placement - im sure it can be done) area. A slug, by its greater mass, will maintain momentum and be more likely to anchor the animal.

Large bore revolvers, lever action 45/70's and similar were fairly popular several years ago when I was up there. I felt perfectly comfortable with a double stack 10mm and hardcast bullets. The local I was staying with, and hunting with, carried a 41 magnum although he said wolves trying to swipe game were more of a threat than bears.