my understanding is as follows
the 444 was designed to take advantage of bullets intended for a 44 mag. Hence these bullets aren't very heavy for a 40+ cal rifle which means they don't penetrate well. Also, the 44 mag bullets were designed to be fired at 44 mag velocities, the 444 pushing them significantly faster has caused a lot of performance issues in tissue. I'd not recommend it for griz.
also, the 45-70 in a lever action. Over-the-counter 45-70 ammo from the major manufacturers is loaded very lightly for fear of some guy sticking it in a springfield trapdoor rifle made just after the civil war and blowing his fingers off. Back in the 1950s when an old springfield trapdoor, at 80ish years of age, would have been encountered from time to time, this was reasonable. It isn't now, but that's the way things ahve always been done...
However, if you are a reloader, or if you purchase specific loadings from some small ammo makers, there is what is considered "power level two" which is significantly more potent than the soft 45-70. It is designed specifically for modern lever action rifles.
(There is also a power level 3, for extra strong guns like the ruger single shot rifles, there it is loaded to match the 458 winchester magnum, capable of dropping elephant and cape buffalo)
the 450 marlin is for the most part pretty identical to the 45-70 power level 2, except as it is a brand new round no worries about it being put in an old gun and making it explode.
I'd go for 45-70, even in it's softer loading it is still deceptively powerful and potent, and found on many gunstore shelves. Then simply reload or purchase power level 2 shells for your useage.