The additional info you provided - the carrying of a .340 & .375 - puts things more in perspective.
With bears the 45acp would be the weapon of choice to use on yourself - not the bear should things go bad. The 44mag is the only acceptable choice between these two calibers.
However, if I'm carrying either one of the two rifle calibers you mentioned, unless I'm on the ground getting mauled, the 44mag would not be the weapon I would think of using.
One other tip, on a moose hunt where I'm concerned about bears I would not top either rifle with a scope suitable for determining if the moon really is made up of Swiss cheeze. A 4 power is plenty - anything larger is only in the way should you need to shoulder the weapon quickly and fire. IMHO