I use the 44-40, it suffers from a couple of things.
The brass is thin, and extra care must be taken when reloading it.
Obtaining brass, while not as easy as 44 mag is no big deal.
If you go 44-40, you will probably want to reload for power.
I've taken both deer and bear with it, but ranges should be short, as it doesn't have the trajectory for longer shots. 75 yards is what I try to limit it to, with heavier handloads.
45 colt I have no first hand experience with, but as I understand it it has similar issues to those described above, except that the basic factory offering has better killing ability than the 44-40. In it's black powder form, it was used to kill game that we wouldn't even consider trying to kill with it today. Same goes for the 44-40, it used to be considered a moose round.
44 Mag, is the only round of the above that has lots of power in factory form. Indeed the advantages or reloading at least from the standpoint of more power are next to nill. Killing power here is comparable to the 30-30. Trajectory is a tad higher, but at the effective range makes no real difference. That range is probably 150 yards, if the rifle and the shooter are capable.
It is a very effective killer on the game mentioned.
Reloading it will give you a variety of bullets, including lead, including some heavy offerings, in all three of the above.
44 mag has excellent brass, and good brass life for reloading.
*45 Colt, and 44-40 have thinner brass, and shorter brass life, unless you are very careful, and don't really max out your loads.
45 Colt, and 44-40 have an amazing ability when reloaded for a rifle, heavy loads can rival the 44mag in the 44-40, and exceed it's killing power in the 45 colt, if you are a careful reloader. Be advised however that some of these rifles may not shoot those high power loads accurately.
*Starline makes heavier brass, but loads should be adjusted to adjust for the reduced powder space.