The rules are that if you can carry legally in that state (remember that a lot of states don't honor concealed carry permits from other states and issue permits only to state residents), you can carry a gun in a national park. It is, however, illegal to fire a gun in a national park! In other words, why bother--any weapon that will stop a bear is heavy! I haven't yet heard if the recent incident in Olympic National Park, in which a hiker broke a leg and was found only after he fired several shots to alert searchers, will result in the hiker's being prosecuted (I hope not!).

The literature states exactly the opposite of what you claim--bear spray is actually more effective than a firearm. Nothing, of course, is 100% effective against an angry bear. Here's one article. Here's another one. It takes an extremely well-aimed shot with an extra-heavy caliber weapon to down a charging bear. Few people can shoot that well! There have been a considerable number of fatalities of folks who shot and only wounded a bear. A wounded bear is an extremely angry bear!