Currently all I own are .357 Magnums. But their are upsides to the .44 Magnum.
The reason the .357 Magnum does better in the one shot stops are the older design Semi-JHP's (125gr) shattered completely in the body, of the BG. That ment 100% energy dump leading to massive shock to the system. The .44 with it bigger weight, beefier, bullet construction, and more energy results in the round, staying together and results in a total pass through of the subject being shot. Thus the energy dump is less overall. The same thing can happen to the .357 Magnum if one were to use the 158 gr bullets. It's a case of too much, too fast.
To use full house loads in a .44 Mag for HD, is stupid at best and it might just get you killed. The reason the .44 Special gets such a bad rap, is because of their is just the utter lack of good self defense loads on the market, plus .44 Specials were rare in police service, in a market dominated by the .38 special, 45 auto, and the 357 Magnum. Rare usage lead to little data from which to make any conclusion. That and the ammo manufactures load the rounds on the anemic side, even though they could load it hotter and still remain in SAAMI safety spec. That being said there are loads out their that would make it as effective as a .45 ACP. I waould hesitate a second to use it for self defense against an intruder.
Another thing in the .44's corner is if our wonderful and all knowing congress critters were to outlaw hollowpoint ammunition, I'd rather be "stuck" with a .44, than the .357. For My .38 caliber bulliet might expand, but the .44 will never shrink!!! The bigger hole, however slight will always help, matter.
The .44 with it's heavier inharent bulliet weight, will help pentrait deeper in to game, to reach vital orgins, especially on larger nasty critters.
In a rifle with the correct (aftermarket) sights and lots of practice(!) can shoot much farther than you would expect (more than enough to lethal against a human being). How far? The .44, 800 yards versus the .357's 600 yards. Again against a human being. You'll need a ladder sight (like the wild West) or a scope to do this. That being said for hunting theres no excuse, not to get as close as possiable to guarantee success.
The down side is that packing the .44, is hard to hide due to the larger frame sizes needed, and the heavier inherant weight of the ammo adds up quick in the pack. In magnum load heavier recoil, when were talking handguns. Also you'll have to put more lead away, and powder if you want to reload you own ammo for the uncertain future.
The .357 ofcourse is the opposite, and will fill most hunting needs and human self defense needs when used it it's limitations.
Either way the cartidges are good ones dependent upon you needs.
Rifleman 336