The late gun writer Elmer Keith wrote that about 1912, he had a Colt 1851 Navy that would cut cloverleafs at 20 yards. He sat down and rested his wrists on his drawn knees.
Keith said he traded that old Navy for a new .38 Special, and always regretted it because the .38 wasn't as accurate as the Navy.
It's tough to compare accuracy with today's reproductions to the originals. The original had gain-twist rifling: rifling that started out straight and then increased in twist as it went along the barrel.
I know of no reproduction Navies that were ever made with gain twist. They're all standard twist.
I've read a few accounts of people who have fired the old, original guns that the gain twist gives better accuracy than today's constant-rate rifling. But it's hard to find an original with a good bore to test the gain twist rifling. They exist, but they're usually near-perfect and firing them may affect value.
There is one gain-twist cap and ball revolver, made in recent years, of which I'm aware: an expensive, target-grade Remington 1858 .44 made for competition. It has gain twist. I think the price is around $1,000. It's been a few years since I've seen one listed in any catalog or website.
It would be fascinating to compare the accuracy of an old original with gain twist, against a modern reproduction. I've never heard of such a comparison.
And until someone finds one with a near-perfect bore, and is willing to risk devaluing it as a collectible, we probably won't see such a report.
As far as I know, Colt made all its cap and ball revolvers with a gain twist. When the Single Action Army came along, fixed-twist rifling was standard.
As far as I know, the cap and ball revolvers were Colt's last use of gain-twist rifling.