Wow...
A lot of information and debate. Dstoltz, are you confused yet?
We don't even agree on modern comparison of cartridges to help illustrate the difference.
See, I'd look at the bullet weight and velocity, so....
The 177 grain round ball from a .50 rifle is kinda-sorta-like a 170 grain bullet fired from a .41 magnum revolver.
The 224 grain round ball from a .54 is kinda-sorta-like a 225 grain bullet fired from a .44 magnum revolver.
The weights are similar and the velocities are similar.. but that's all...
BUT...., The diameter is larger in the round ball, and the ball is soft lead while the handgun bullets are either very hard lead alloy, or are jacketed bullets, PLUS the rifles are shoulder fired making it much easier to be accurate than using a handgun
FURTHER..., the round ball is round, so it's ballistic coefficient is very poor, however, it's performance on impact with a deer is quite different than any other form of projectile. The performance has been noted many times by men who compared the old round ball to the new, heavier, pointed bullets....the round ball does surprisingly well.
So here's some information, some a reiteration of the previous responses,
Modern hunters have a distance advantage and all weather capability over traditional muzzle loaders (at least on paper they do). Because they choose to take advantage of the option to be able to shoot to 300 - 400 yards, even when it's raining to harvest a deer, they have to use modern bullets. They then usually rely on velocity to keep the trajectory variation small, and they usually rely on the bullet deforming into a larger diameter to cause the instant, traumatic damage that harvests the deer.
Traditional Muzzle Loaders because of the older technology aren't going to be able to get that flat trajectory, and due to physics, what speed is given to that ball is quickly shed. So soft, pure, or almost pure lead is used, and the ball starts out large (compared to a modern bullet) at the start. So the modern guy often is delivering a .224 to .358 bullet that travels to 300 yards, and wants it to "mushroom" to .45 or better on impact, and wants the bullet on impact to get to that size fast to then do the necessary damage. The traditional hunter is launching a bullet to travel 100 yards or less, and that bullet is already .45 diameter (or larger). So any deformation is a bonus, and the traditional muzzle loader hunter simply wants that bullet to go deep enough into the animal to do the necessary damage.
Shot placement is always the primary factor, modern rifle or traditional muzzleloader. (imho) The modern guys rely too much on bullet deformation at impact to compensate for poor accuracy from their rifle and ammunition (or poor marksmanship skills).
THEN you get into the
nitty-gritty village....
The .440 is the lightest of "the big three calibers", so is often going faster, and kicks less, but has less inertia on impact, but reliably kills deer...
The .490 round ball gives more impact weight, and recoils a bit more, but has a better trajectory than a .530 ball, but reliably kills deer...
The .530 round ball usually recoils the most, but has the highest impact weight, but the poorest of the three trajectories, but reliably kills deer...
All of the above is a simplistic explanation. There are a lot of other areas where the hunter can modify a variable to get some different, desired results.
The deer likely isn't going to notice such differences.
LD