The Remington carbine, loaded with full charges and conical bullets, is the equal of modern 45 Colt pistols. In other words; there's plenty of horsepower there to get the job done. With a 240 grain bullet in the carbine I get a full 600 foot pounds energy.
Also, with a minimum conical bullet weight of 200 grains (I've used up to 240 grain bullets in the Remington) you're throwing heavier lead from your 44 than a 50 caliber round ball (which is about 180 grains). That weight gives you plenty of penetration, even though it's going a bit slower, so make sure that penetration hits the things it need to hit inside.
I any case, it's not so much the gun as the shooter's ability to put the bullet in the right place. A 35 grain bullet placed in the brain pan from a 22 mini revolver beats a 720 grain bullet placed in the gut from 50 BMG any day. Shot placement trumps raw power.
Understand your prey's anatomy (where to put the bullet for a clean kill), know your personal limitations and operate within them, and you're good to go.