Maybe obvious, but compared with any handgun a 300 Win Mag is dramatically more powerful. As noted, any Elk bullet should work at close range.
If you are someone who hunts without one in the chamber, I'd strongly consider also carrying a sidearm. Even a 9mm can kill a Grizzly based on the results of shootings. Sure, bear spray can be good but it won't stop a Grizzly, it only discourages it and only works in the right wind or no wind. A handgun is also useful to have a gun on you while you are processing your kill.
That being said, most people won't come across a Grizzly while hunting, so how real the danger is up to you to decide.
If you are someone who hunts without one in the chamber, I'd strongly consider also carrying a sidearm. Even a 9mm can kill a Grizzly based on the results of shootings. Sure, bear spray can be good but it won't stop a Grizzly, it only discourages it and only works in the right wind or no wind. A handgun is also useful to have a gun on you while you are processing your kill.
That being said, most people won't come across a Grizzly while hunting, so how real the danger is up to you to decide.