Snowsniper8, I have a .357 on my ATC, as my back up gun, but I seldom carry it, preferring the .44. There aren't any factory .357 rounds I would want to use in a bear defense scenario, and anything you can do to improve the .357, such as choosing heavy for caliber flat nosed bullets can also be done to the .44. If you were considering a 40 oz handgun, there might be an issue with the .44's recoil, making the .357 the better choice until such time as you acquired a taste for it, but recoil isn't an issue with the .44 magnum when its chambered in a rifle.
Killing a bear in a defensive situation with a small cartridge like a .357 requires a good knowledge of bear anatomy, good marksmanship and gun handling skills, and a cool hand. The fact that you are asking the question suggests that with your level of experience you're not up to it. A lever action can be a good choice as a defensive arm, but a .44 is the pistol cartridge you should be considering, or a rifle cartridge like the.444, .450 Marlin or a .45/70.