I'm guessing your question somehow ended up in the wrong forum because I can see no logical reason why anyone would carry a rifle chambered for a standard revolver cartridge as grizzly protection. As someone pointed out, the 44 Magnum is comparatively weak next to even the lowly 30-30 Winchester. If you're going to carry a rifle or carbine exclusively for grizzly protection, carry something like a 45-70, a 338 Win Mag, a 375 H&H, or a 30-06 loaded with heavy, 200-grain bullets.
Second, you didn't say where you are going. But seeing as how the only significant grizzly populations in the lower 48 are in and around Yellowstone and Glacier National Parks, I'm guessing you're headed way up north, like Alaska maybe. Every time I hear of someone shooting a grizzly around here, the person ends up in court. Or at least there's an investigation. If you shoot a grizzly in the lower 48, you had better be ready to show claw marks or remember the 3-S rule - Shoot, Shovel, and Shut-up.
If you are going to carry a revolver for grizzly protection, and your choice is between a 44 Magnum and a 357 Magnum, I'd go with the 44. Load it with hard cast, 300-grain Keith style semi wadcutters over a stout charge of WW296. That's what I carry while backpacking. Although, I've never even seen a grizzly outside of a national park. But I have used that load to kill a couple of mule deer during season. At a little over 30 yards, it will exit a large buck after breaking a rib on one side and the shoulder on the far side.
Even with my heavy loaded 44 Magnum while backpacking, I figure my first line grizzly defense is avoidance. My wife and I both carry bells and whistles. And we use them while traversing areas where we can't see very far ahead. My second line of defense is a large canister of pepper spray. Yeah, I've heard all the jokes about grizzly scat having little bells and whistles in it and smelling of pepper spray. I've also heard the ones about filing the sights off my handgun so it won't hurt so much when that grizzly shoves it up my you know what. So, I guess it's a matter of opinion - just like whether a 12 guage loaded with slugs offers enough penetration or not. But from accounts I've read, most grizzly attacks come very fast from a distance of less than 50 feet. I love handguns, particularly large bore revolvers and I've used them for over 40 years. But with a fast, angry, and powerful target at 50 feet or less, I'll take my chances with a big bottle of 20% capsicum pepper spray thank you.