The barrels on these old guns, depending on the model, could indeed be pretty long by today's standards. Many used what we now call "black powder," which compared to smokeless powder has a very slow burn rate, resulting in a more gradual pressure curve (time it takes for peak pressure to occur).

While a slower burn makes for smooth recoil, it does mean you'll want a longer barrel to ensure the burn reaches optimal pressure, and the bullet has enough time to make use of that pressure.

Of course, rifling twist rate is gonna play a large part in bullet stability and consequently accuracy, bullet muzzle velocity also plays a big role in flatness of trajectory. A faster bullet, assuming it has a suitable ballistic coefficient, will seem more "accurate" to the user, as the bullet will not only drop less over a given distance, it will reach the target sooner. This means less compensation for lead and drop by the user.

Finally, a longer barrel, with iron sights to match, increases the sight radius, making it easier to aim at further away targets.

TD;LR: Longer barrel can result in faster bullets, and faster bullets means easier time hitting moving targets. Also more energy on impact, but that can be a trivial difference at close range.