Well if you are limiting the Muzzle Loader to shooting a PRB "patched round ball" then the advantages will lean twords the cartridge shooter in distance due to the ball has only an effective range of maybe 150 yards because of the ball having a lower sectional density & ballistic coefficient than a conical firing out of a cartridge weapon.
.45 caliber Muzzle Loader w/ 28" barel 1:48 twist.
.440 128gr. PRB 60gr. FFG Goex
Muzzle = 1614 fps. - 741 ft. lbs.
100 yds. = 965 fps. - 265 ft. lbs.
.45-70 rifle w/ 30" barrel 1:18 twist.
.457 405gr. RFP 60gr. FFG Goex
Muzzle = 1182 fps. - 1255 ft. lbs.
100 yds. = 956 fps. - 820 ft. lbs.
That's just ballistics at 100 yards, then you have to concidder the sights for each weapon where as we moved forward with technology including the area of sights where the average shooter could acquire the sight picture more efficiently than compared to the muzzle loader weapon of the period.