Lets look at this realistically.
With a 50 cal or a 54 cal muzzleloader you can shoot 44-45 cal bullets up to about 300 grains. Velocity is typically around 1800 FPS for accuracy. You can go faster just as you can with patched round balls, but after a certain point (which is usually about 1800-1900 FPS) the accuracy is poor, so that is the range of velocity for usefulness.
Now a 54 cal rifle shooting balls fires balls of .530" or .535" which is about the same size as an expanded 45 cal pistol bullet. The bullets weigh a bit more, so if we look at this mathematically you can see that the bullets will have a small edge over the balls in both weight and in flatness of trajectory.
But when we step up to a 58 cal we get the ball up to 270 grains. Still a bit lighter than the heaviest 45 cal bullets used in sabots, but the velocity is the same, and the wound made by the 58 cal is now bigger if the ball is hard, and a lot bigger if the ball is softer.
When we go to a 62 cal or a 66 cal there is no longer a contest.
Now there is the issue of the would channel in the animal. If you look at the pictures of the perfect mushroom of the premium bullets and you cover the shank of the bullet with your finger what does it look like? Well,,, the front end looks like a ball.
So we take a 45 cal bullet and turn it into a 50 or 54 cal ball when it hits the animal. The only thing a bullet does better is fly. Not kill. But to about 100 yards it makes no difference on game. It's flatter, but not much flatter.
If you shoot them at 200 yards the bullets will often not expend totally and then the ball again had the advantage in killing the game, but may be harder to make the hit if your range estimation is off a bit. The ball is the size of the expanded pistol bullet at every range and it doesn't need to expand. So do. So that can make them even bigger in diameter.
You see guys, bullets in muzzleloaders are not a new thing. They were all the rage in experimentation from the 1830s to the 1870s too. The old timers knew that they had some advantages but were a mixed blessing. If you want to read "the Bible" on the subject, see if you can find the book "The Sporting Riles and it's Projectiles" by James Forsyth which was printed in 1863. He and his contemporaries killed more game in 10 years than most of us will have killed collectively in our lives and did it all the the most modern rifles available at the time,,,,,,,,which were all muzzleloaders.
They knew what worked and what didn't
As for me, I am into traditional muzzleloaders, and the modern in-lines and plastic stocked rifles hold no interest at all for me. I do not condemn them. I just don't find them interesting at all. But as the former CEO of Cast Performance Bullet Co, I know a bit about how well they work. We made bullets specifically for them and mated them to specific sabots for specific clients and customers. I did a LOT of testing of them back them. They work and work well.
But for me to say they work better on game animals out to about 150 yards then traditional muzzleloader is just not true.
A 50 cal with a hard ball shot at 1800 FPS is still just fine on deer, and even kills elk well. My friend Randy has killed 6 elk with his 50 cal, all with hard balls (cast from WW metal) and EVERY ball passed clear through leaving only a large hole behind it. No balls were recovered.
I have killed deer elk and antelope and a few domestic sheep, horses and cows with muzzleloaders running from 50 cal to 66 cal. Again, I use Wheel Weight lead for the balls and I have never had a problem. I also have recovered few balls.
I did recover one from a 1900 pound buffalo, and I also recovered some 54 cal balls from domestic cattle, but all fell to the shots and all were dead within a few seconds of the shot.
I am building 3 bullet rifles right now. All British style. All made for 45 cal RIFLE bullets (shooting bullets from 350 to 500 grains as you would use in a 45-70 to a 45-120 Sharps) At the same velocities as you can get from the breach loaders, these bullets will kill just as well, and the animal doesn't know or care what end of the gun the bullet was loaded from.
So I have knowledge of how well these things work, but for deer and elk I can't really see any real-world advantage from a saboted pistol bullet over a 54 (or bigger) round ball.
If you want to shoot 200 yards and farther with a muzzleloader pistol bullets are not the answer. Sure ---- they work, but they don't work any better at killing game then balls at that range, because they are smaller in diameter and often don't expend at the impact velocity of 1000 FPS or less.
54 cal balls often don't expand either but they are 54 cal, so they don't need to.
If you want to kill game at 200 yds and farther with a muzzleloader you should have a bullet rifle made to shoot rifle bullets.
I recommend 38, 40 or 45 calibers, depending on the game you want to kill.
Some states have regulations about bore size, so even though a 45 cal bullet rifle may have the same ballistics of a 45-120 sharps (good enough to kill bison at 500 yards) it may not be legal for 100 pound deer in your state, so check the regulations first.