How accurate ? That depends .
Really it has less to do with projectile rifling and sites as it does with the shooter . There are many period accounts of 2-400 yards with round balls on humans . However I would point out we cant really use this as humans are considerably of weaker frame them most all wildlife
Given a person who has spent time learning their rifle . Mind you a rifle that that shooter has either purchased or specifically built for their intended purposes . This is the point where rifling and projectile come into play . However I submit to you that even if a give rifle is designed to be capable of holding a 12x12 group at 1000 yards does not mean that shooter will ever be capable of shooting anywhere near that distance .
Why ? Simply put traditional muzzleloading is in most cases not a weapons type that can be just picked up or shot only a couple times a year and get results at distances past 150 .
However , the more technologies we add to that weapon the less proficient the shooter has to be .
Example would be adding a 4X variable scope to a slow twist rifle shooting a round ball . If the scope is set so at to zero that load at a given yardage and the shooter does his part they will get an acceptable pattern.
Now take that same rifle , replace with open sights and suddenly minor flaws in ones shooting technique becomes greatly noticeable to that shooter and a major problem . Unless the shooter practices they probably even with good eye sight will never achieve the same level of accuracy at the distant ranges that the scope allows them
We also have to add in the over confidence that using a scope gives at greater distances .
This brings up the question of how accurately can a shooter using a traditional muzzleloader shoot using open sights . that’s also dependent on physical ability as much as visual . IE is the rifle rested . If so what type of rest . If off hand how is the rifle built can the shooter properly steady their shot , was the rifle design meant to be shot this way .
We know from reports as well as documented targets such as those I have posted bellow that a slow twist rifle , shooting low charges with open fixed sites with just an elbow rest can if the shooter has done their work hold nickel to silver dolor groups at 100 yards . 8X11 at 200 and beyond .
With a faster twist shooting conical even of calibers 50 caliber and larger 5 to 6 inch groups at 4 to 500 yards if rested and using lighter game loads .
Lastly are modern weapons more capable then traditional muzzleloaders ? For the general public IMO yes unless confined to open sights and given projectiles . The ignition itself only comes to play as a reliability question . To that I say if a person spends the time to learn their rifle . Becomes proficient with it then the reliability issue is also not any issue at all . So why then the allure of modern designs ?
Ill let that part stop right there for you to think about .
Here are some recorded targets for you all to consider . Some of you may have seen these others probably not .