And for what it's worth, I shoot a paper cartridge 1863 Sharps carbine in competition. It's the fastest gun on the line in terms of loading in our competition and quite accurate.
Muzzleloaders are slow, duh, cartridge guns faster but within that genre there are differences. Of the cartridge guns, Sharps, Smith, Gallagher, Starr, Burnside, Maynard, Spencer and Henry, the Henry is hands down the fastest but it is the first fairly large scale production of what we consider as a "cartridge arm" today with completely self contained ammo. The Spencer is right behind with completely self contained ammo, meaning primer, case, bullet, powder in one unit. The Henry completes the loading cycle with each stroke of the lever and is ready to fire. The Spencer is ready after cocking the hammer for each shot and is a bit slower and it also holds less ammo than the Henry.
Following that are the others, but each is a percussion gun and requires the use of a percussion cap to be placed on the nipple for firing. Each is a single shot using cartridges. Each, except the Sharps, has to have the spent cartridge removed in loading. The Sharps, you just drop the block, shove another round in, raise the block, cap and fire. In short, one less step than the rest.
In our competition, we have a Carbine class that permits muzzleloaders, Smiths, Sharps, Gallaghers, Starrs, Maynards and Burnsides in one class. Spencer and Henry each have their own class. The competition reality is, in terms of accuracy, the muzzleloaders can be extremely accurate, but have a much slower rate of fire. I have an Enfield musketoon that is easily a sub 2moa gun in .58cal. My Sharps is close, but not quite there in accuracy but what it gives up in accuracy is far more made up in speed. The Musketoon is at best, 4 shots/minute. The Sharps, 10+.