Both cartridges will probably work equally well for deer hunting, although the .45 Colt has the edge in a toggle link rifle due to using heavier bullets at low chamber pressures.
For reloading the .45 Colt has the edge again since it uses a more modern wall thickness that is more forgiving to resizing, bullet seating, and crimping. The .44-40 brass is thin and takes care to load.
These days factory loaded .44-40 is hard to find and expensive, while .45 Colt is a standard shelf stocked load. (everything may be hard to find these days, but just saying...)
The modern .45 Colt rim works excellently in all lever guns, thanks to the fouling groove which presents plenty of rim engagement for sharp beak extractors, unlike the 19th century .45 Colt case which had hardly any rim at all.
As has been said, blow-by only happens with pipsqueak cowboy loads in .45 Colt. It does not happen in standard velocity factory loads or even with cowboy velocity factory loads.
I own both .44-40 and .45 Colt lever guns and both cartridges seal equally well.
Last edited by saddlegun; 03/30/21.
