Would a handgun be enough to stop a grissly? (aside from making a lucky shot) I've always wondered about that.
Shot placement, speed and situational awareness trump caliber every time.
With that said, typical defensive loads for humans are not appropriate, as they're designed to expand and limit over-penetration. Bears have much better natural armor than humans, so a large jacketed (JSP better than FMJ) or hard-cast lead bullet is better to achieve enough penetration.
The prevailing wisdom seems to be that a .357 Magnum loaded with heavy JSPs would require precision hits on the central nervous system to reliably stop a bear. Under stress, few people can make precision CNS hits on a charging bear with a handgun. As a master-class competition handgun shooter, I would be doubtful of my ability to make such a shot.
A .44 Magnum or .454 Casull is more appropriate -- for those that can accept the weight and are capable or shooting them effectively. I'd rather have a shotgun loaded with slugs.
It's worth repeating that your best move is to avoid confrontations with bears. It's also worth repeating that you shouldn't carry firearms anywhere unless it's legal to do so and you are trained to use them safely and accurately.
Lots of people, most of whom who have never shot a grizzly, have theories about the best caliber. No handgun is really good bear protection. The only real advantage of a handgun is that it is lightweight (relatively speaking), and you might actually have it accesseble when you need it. Yes, people have successfully protected themselves with a 44 Mag, but truth be told a 44 Mag is pretty weenie bear medicine. Even most 454 Casull loads deliver less muzzle energy than a 30-06, which most people who have experience with bears would consider the minimum rifle cartrige for bears.
Keep in mind that a grizzly bear is a very tough animal. Big bones and massive muscle, under a thick layer of fur and fat. Their brain is actually quite small, relative to the size of their head. The skull is very thick, and the front of the skull slopes back at an angle, like the frontal armor on a tank. Unless you get very lucky, shooting a bear in the head will just mean a really pissed off bear with a bad headache.
If you choose to carry a firearm for bear protection, the best advice is to carry the biggest, most powerfull rifle you can shoot well. In Alaska, the two most popular guns for hunting big bears are the 375 H&H, and the 338 Win Mag. A 12 gauge shotgun with rifled slugs is not a bad choice for protection. On hunts I have killed a brown bear with a 338 Win Mag loaded with 250 gr Nosler Partition bullets. I've also killed a black bear with a 30-06 with 220 gr bullets.
These days however, I generally only carry bear spray when out hiking. It is much lighter weight to carry, and has been shown to be on the average at least as effective as firearms. That is my choice, and I spend a lot of time in bear country.