Hard to offer an inclusive, objective and fair opinion. Few if any people have shot all the varieties in comparable condition. My main interest is in older military rifles that span the era from the Mexican War, through the Civil War but have owned and shot a variety of the ones mostly being covered in this thread- maybe Span-Am War through WWI and WWII.
Prior to the US M1841, most blackpowder military arms were smoothbores that shot single round ball or some combination of ball, buckshot or shot. My experience with these has been they are not very accurate compared to rifled arms. However that doesn't say they were ineffective on the battle field. I have two original 69 cal US military smoothbores- one flint and one percussion. I would not like to be shot at by either gun by an experienced shooter on the battle field at any range less than maybe 250-300 yds. Less than those ranges and the hit ratio will get progressively higher for my taste, probably approaching 100% at 75 yds or less.
And obviously some smoothbores will be as accurate as any one particular more modern rifle that may have a worn out bore or shooting bad ammo.
In any case all these comparisons need to be made apples to apples.
All my old military, both rifle and smoothbore, are original. I have a 54 cal US M1841 rifle and two or three 58 cal US Model 1861/63 rifle muskets that at +/- 50 yds are as accurate if not more so than most modern smokeless cartridge military rifles comparing all with original open or iron sights. In some cases there is little doubt that "battle" sights may be the limiting factor for accuracy with any rifle. I shoot these originals with the components they were originally loaded with- musket cap ignition, blackpowder charges that approximate the caliber in grains and near pure lead hollow base Minies.
From the early 1890s to the early 1900s an explosion of modern smokeless cartridge military rifles were being developed by many countries. Of the ones I've owned or shot, the 4 groove 03 Springfield and the 4 groove Remington and the 6 groove S-C 03-A3 Springfields have consistently been the most accurate. The couple of 2 groove Remington 03-A3 I've had were not as accurate as any of the 4 or 6 groove Springfields- all other things being equal like bore condition.
But no matter the rifle or country of origin, all this remains somewhat anecdotal because the sample sizes are small and I haven't shot, and I would say very few have, even a majority of the ones out there. Plus, original military arms in comparable and good to excellent condition are hard to get ahold of to begin with. The most accurate of all military rifles I've owned, dating up through the WWII era, was a really high condition US 4 groove Remington 03-A3 Springfield. I'm sure the aperture sight helped but still little doubt about how exceptionally accurate it was.
