Most feel that the 44 will give you tons of bullet options and plenty of power while the old 45 colt, while plenty powerful, is easier on the ears and wrist. I like them both and would have a hard time saying which one would win "best overall" deer hunting round.
There are lots of gun choices in both calibers. However, the 45 is offered in some interesting choices. An example of this would be the Taurus Judge. This might end up being a great hunting piece if you can find one that hits point-of-aim with a solid heavy cast bullet (as they have fixed sights). These shoot the 410 shotgun shells too. T/C offers this combo in a single shot pistol version. NEF makes a single shot 45 colt/410 shotgun in a rifle. There are others offered in this configuraton as well.
So, does this make the 45 a better choice? Being able to shoot 45 colts and 410 shotgun shells out of the same gun could be pretty handy. Sometimes it not just the round itself that makes it great but rather all of the other factors that revolve around that round.
Other things to consider are the guns that shoot both the 454 and the 45 colt. Furthermore, there are guns that shoot 460 S&W, 454 and 45 Colt. Talk about versatility. What type of combo are you getting out of a 44? I know you can shoot 44 specials out of them but that's just about it, as far as the common stuff goes.
What barrel length is best, you ask? It's my opinion that barrel length matters when shooting steel gongs at 200 yards but makes almost no difference, at 20 yards, on deer sized game. I would use a Ruger Alaskan, in 45 colt, for deer hunting if it were legal in Ohio. Some guys like the longer sight radius of a longer barrel and they certainly look better on paper from an energy standpoint. However, I tend to shoot a shorter barrel better. Why do you almost never see 7.5" barrels in cowboy action shooting? It's because folks want to hit their mark(s) and the shorter barrels pop out of a holster faster. Most folks prefer the balance of a shorter barrel when they take the time to give them a chance.
My state places a minimum requirement of 5" on barrel length for deer hunting. Which is dumb if you ask me. They measure revolvers from the start of the barrel and not the back of the round. While they measure single shots and automatics from the back of the round (rim). Here is an example of another thing that doesn't make full sense: A S&W 460V, shooting 45 colts, with a 5" barrel is legal here (even though there is only 4" of rifling due to the compensator) but my 45 colt Redhawk with only 4" of rifling is not legal. Two guns, same amount of rifling, same bullet....and only one of them is legal for hunting. This is just one example.
You asked your question with the mention of factory ammo. I don't know about other parts of the country but around here, 45 colt ammo flies off of the shelves. I do seem to always see 44's. This might give the 44 an edge. If you are going to be shooting factory ammo then it helps to have it available in stores for purchase. My dad started shooting 45 colts 30 years ago because he could do a lot with the ammo and it was a third of the cost of 44 mag's. Things have changed.
A lot comes into play when looking at a hunting revolver/caliber. I'm just glad that we have all of the options that we do. Now, if we could just get the law makers to stop over-regulating the hunting tool requirements. A guy can shoot 2" off-hand groups, with hot 45 colts, out of a 4" barrel and that is not legal to take hunting in Ohio. The same hunter can shoot 10" groups with a 6" GP-100 and that's legal to take. How is this common sense? They should trust that most people, who hunt, are really into the sport and we want to use the most accurate tool available. Even if that tool has a barrel that is 1 inch shorter than "legal" length. Ok, I'll get off of my soap box, now. I just had to get all of that off my chest.