Although I have not shot the old guns farther than 600 yards, I feel qualified to discuss the matter. (Don't we all?)
I voted Highwall because the lock time is a theoretical advantage and the self cocking action is a real advantage when shooting under BPCR Metallic Silhouette time limits.
My main match rifle is now a Jap Browning "highwall" BPCR model with US Badger barrel. Caliber is .40-65 because that is all the recoil I can enjoy.
Note that the Miroku guns, now "Winchesters" are not faithful copies of the original. They look similar, are at least as strong, and shoot well, but are mechanically different. They lack set triggers or much adjustment of the single pull but can be tweaked to about a two pound pull which is fine for me. Stock attachment is by throughbolt instead of tang screws, a definite improvement. (Which is also available from Meacham on their BPCR models that are otherwise close copies of Winchester.)
My previous match rifle was a real Winchester Single Shot .38-55 which is a joy to shoot but did not always knock down the metallic silhouette rams (46 pounds, 500 metres.)
You can get highwalls from Winchester/Miroku, Meacham, Ballard, C. Sharps, Uberti, and Pedersoli. McGowen Barrels is still trying to bring their "American Gun" to market.
As rcmodel says, Sharps 1874 replicas lead the pack.
Good barrels and good quality general construction trump the theoretical disadvantages of the heavy side hammer and its slow lock time. A spare firing pin in the range box would be a good idea, though.
Shiloh turns out a great quality rifle with a lot of options. They have good "customer service", legions of loyal and vocal customers, and their own internet board. C. Sharps, which used to be part of the same company, produces another fine rifle right down the road from Shiloh.
Pedersoli sends in decent quality Italian reproductions.
There are other imports but they are seldom seen in matches. Quality is variable to put it kindly.
There are or have been a couple of other small US makers but their output is small and their rifles seldom seen.
There is a very expensive German made Sharps, of all things.
The 1874 is not the only Sharps.
C. Sharps makes repros of the rare 1875 Sharps. It lacks the movie credits of the 1874 but is a good solid rifle with the advantage of being the least expensive American made BPCR. Its Badger barrel will shoot with any.
Axtell builds (Built, maybe, the riflesmith.com site is down and there are rumors of Mrs Axtell offering the company for sale.) reproductions of the 1877 Sharps which can only be described as sensuously attractive. C. Sharps now lists the 1877 if you have a lot of money to throw around.
The Remington Rolling Block was the other main buffalo hunting and target rifle of the 19th century. It was made in tremendous variety but a lot of their production went into military rifles for foreign lands.
If you want a new one, I would give the Remington Custom Shop version a pass. The few I have seen were not of a build quality up to the high price.
If you want a nice Rolling Block, Dave Higginbotham's Lone Star Rifle Co. of Texas, America turns out a very good one, with a lot of options. He will even fix up your old real Remington to look and shoot good.
The Pedersoli Rolling Block is ok.
The Trapdoor Springfield, being a military rifle, can be a lot of fun but is not seen in serious competition except by a few rugged individualists who just want to prove It Can Be Done.
"Other" covers a lot of ground.
When I shot at Bon Aqua, Tennessee, I saw a lot of Ballards. This largely because the guy who owned the range had set up as a Ballard dealer and could offer good prices for good rifles. They are not otherwise real common but do have their points, like stock throughbolts, fast lock time, positive headspace control, and good triggers. It is not a real strong action but that matters only to the varmint hunter, not the BPCR shooter.
CPA turns out newly made Stevens 44 1/2 rifles. That is a good accurate gun, and probably the easiest to swap out barrels on; you can even get a .22 barrel and a rimfire breechblock. It was late in the single shot rifle era, used mostly for Scheutzen, and lacks the cachet of the old buffalo guns. Nothing wrong with it as an actual shooter, though.
BZ Arms makes a replica of the Remington (No 3) Hepburn side lever single shot. It is another good rifle even though not seen nearly as often as the Sharps or Rolling Block.
Then you get into the REALLY scarce stuff.
Steve Earle makes replicas of the Frank Wesson single shot actions. You have to get the rifle completed by an independent gunsmith but they sure come out nice. The Wesson No 1 is an almost line for line double of the Alex Henry sidehammer. The Wesson Midrange is kind of odd looking but I bet it will shoot.
There is a new outfit making Peabody rifles in continuation of the old Providence Tool Company. This is the original sidehammer Peabody design, usable in NRA Silhouette competition, not the hammerless Peabody Martini... which was adopted as the Martini Henry, using the names of the hammerless striker designer and the barrelmaker, completely losing sight of the origininator of the tipping breechblock action.
Phew.
There are probably some more that I do not know of or recall offhand.
Plus, there are gunsmiths who can make an old single shot look and shoot like new. I have seen original Hepburns, Rolling Blocks, and Winchesters in use.
Let's talk briefly about SHOOTING the darn things.
My interest is in BPCR, Black Powder Cartridge Rifles.
Cast bullets and real black powder will actually get the best target performance out of these old guns. Nitro will give higher velocity if you wish to hunt something bigger than buffalo, but black is better otherwise. Quality casting is necessary and match grade BP loading is demanding, but that is part of the fun of it.
You will find that a 405 grain .45 bullet is light for even 400 yards. The Army went to 500 in 1881; modern shooters are up in the 525-540 gr range for most such use.
