Remember - a 44 magnum pistol only has a fraction of the power of a 30-30, which few would choose to hunt bears with. That said, in a full metal jacket a .357 would do some genuine harm - if you have the nerve to aim carefully, or if you shot it while being mauled...
I think the park service rules are like military regulations - for the guidance of the wise and the strict adherence of fools. When hiking in Glacier, Yellowstone etc, a good concealed handgun could be a very good friend.
In fact, even a 22 can be a good friend. Years ago, when hiking in a National Forest, I returned to my car to find 8 drunk teen-agers sprawled on it. They lowered their bottles and started to surround me when I pulled out my trusty S&W 22-32 kit gun. Having fired thousands of rounds thru it, I had no doubt I could shoot 6 of them in the head. They must have agreed, 'cause they backed off and 'let' me get in my car.
Not all varmits have 4 legs...
If it is concealed it will be difficult to deploy in a hurry. Also, if you do shoot and injure or kill a bear in a national park, you would need a hell of a good lawyer and some deep pockets, the feds would go after you like you were a child molester. Don't think they would have pity on you because your life was in jeopardy.....they would not.
Here is a paste from Remington's online ammo catalog. As you can see the 'energy' of a .30-30 and .44 mag, particularly at the muzzle (where self protection shootings take place) are pretty close. Of couser you specified power and there is not an agreed upon 'power' formula for bullets.
One of the oldest and frequently cited is the Taylor Knock Out Factor, which Mr. Taylor a professional hunter created to mirror his observations of different bullets on charging African game.
TKO is calculated by multiplying bullet weight in grains X muzzle velocity X caliber divided by 7000. Using this formula the .44 Mag has a TKO of 24 to the .30-30's value of 14.
Note: the muzzle velocity for the .44's here are high because it's for rifle length barrels like the many lever actions chambered in this round.
In summary I think you can make a pretty good case that the .44 mag is a better bear stopper than a .30-30, in similar guns, and maybe the equal in the guns more typical for each (ie: revolver vs. lever gun )
30-30 Win.
44 Remington Magnum
Index No. Cartridge Type Wt. (grs) Bullet Style Primer No. Ballistic Coefficient
R30302 Remington Express 170 Soft Point Core-Lokt® 9 1/2 0.254
R44MG3 Remington Express 240 Semi-Jacketed Hollow Point 2 1/2 0.166
VELOCITY (ft/sec)
Cartridge Type Bullet Muzzle 100 200 300 400 500
Remington Express 170 SP CL 2200 1895 1619 1381 1191 1061
Remington Express 240 SJ HP 1760 1380 1114 970 878 806
ENERGY (ft-lbs)
Cartridge Type Bullet Muzzle 100 200 300 400 500
Remington Express 170 SP CL 1827 1355 989 720 535 425
Remington Express 240 SJ HP 1650 1015 661 501 411 346