The best way to start a good conversation here is to say one cartridge is 'better' than another.
Personally, I think a 5ga punt-gun beats everything mentioned so far. Mmm imagine the slugs for one of those. That'll handle elephant, tiger, lions, blue whale, Jupiter, a flock of snow geese a mile up, and grizz.. don't forget grizz. 5ga... it'll kill anything you can manage to aim at well enough to hit. within and exceeding 2 light years away.
ROFLOL!
Best alternative round yet posted! Where can I get one? I have seen 4 gage guns, and 8ga., even a 2ga., but not a 5ga.
While I prefer the 30-40 Krag for deer or even elk at reasonable ranges, there is no doubt that the the 30-06 is a superior cartridge. It has superior ballistics to the 8x57 Mauser, more velocity and delivered ft-lbs of energy for given bullet weight.
As for the 45-70 being superior for bear? The ballistics don't look good. I assume we are talking rifle ammo, not handgun. While the 45 is a big heavy round, it is very slow, and the delivered ft-lbs of energy are low. I have no doubt it would do a number on a big brown bear, but a 30-06 would do an even better one. I know, I know, with the right "custom" load, it will do anything, it is the most awesome round alive, much like the 8x57 crowd.
I don't mean to put down the 45-70, or the 8x57, but a more flexible or effective round than the 30-06, would be hard to find. It is quite capable of taking out any North or South American game, and most African game as well.
While it may not be the most effective squirrel gun imaginable, if I had to have one rifle, it would be a 30-06, hands down.