I would go with the .44-40, for nostalgic reasons if nothing else.
The .45 Colt has greater recoil, especially in the Colt Model P.
The .44-40 has been taking deer-sized game and smaller for 130 years, when fired in a rifle. Range against deer should be limited to 75 yards with the carbines and perhaps 100 yards with the full-length rifles --- not because of the meager difference in velocity between a 20 or 24-inch barrel, but because the sight radius on the carbine is shorter and makes precise bullet placement at 100 yards difficult.
As a defense round, the .45 Colt has a reputation as a brutal manstopper. But the .44-40 also has a reputation as a good manstopper too.
Recoil is slightly less with the .44-40, which allows for a quicker follow-up shot if one is needed.
The .44-40 launches a 200 to 215 gr. flatpoint bullet at 900 to 1,000 feet per second at the muzzle, depending on whether you use black powder or smokeless loads. That's nothing to sneeze at.
The .45 Colt launches a 250 gr. pointed bullet at 900 to 1,000 feet per second at the muzzle, depending on black powder or smokeless load used.
That's nothing to sneeze at, either.
But do you need all that power? If X is good, is X-Plus better? Your sole concern is putting the aggressor down. The .44-40 has a proven track record of doing that, so why put up with increased recoil from the .45 Colt.
Don't get me wrong! I dearly love my Ruger Blackhawk .45 Colt and my early (circa 1874) Colt Model P "Peacemaker" but when it comes to dropping humans at 25 yards or less, the .44-40 will work just as well.
I've heard that many of the .45 Colt lever rifles are persnickety about feeding, whereas the .44-40 is not. This too is a strong recommendation for the .44-40 in a rifle for game at short range and people at even shorter range.