I've owned two Bisley-style revolvers manufactured by USFA and a Colt SAA, all in .45 Colt. They were interesting to compare, although I'd be hesitant at this distance in time to compare the finishes between the Colt and the copy. The copy in this instance was made in the original Colt building, I believe.
I'm not so sure if the Bisley grip improved on the regular grip or not. It may have had it's origin in the Colt 1860 Army revolver but I've never handled one of those, original or otherwise. I did own a Ruger Bisley, however, and I believed it had the best grip of any of them. Of course, Ruger had maybe 80 years to get the design perfect, even though it didn't take that long. Ruger also made small frame single actions with a similiar grip but I never had one.
One thing about the Bisley, I believe, was that it could not be fitted with a solid one piece grip like the SAA and neither could the Ruger, any Ruger single action for that matter. The SAA I had came with hard rubber grips and it left with the same grips. I'm afraid the USAA Bisleys both suffered cracked grips and I doubt it was because of my powerful hands holding it. But otherwise, they all worked fine. Not so with the one Italian made .45 single action, on which one of the springs broke almost right away. The shop replaced it with a Colt made spring.
I have seen Bisley models show up in movies. The movie the Grey Fox (with Richard Farnsworth) featured a Colt Bisley (which the character chose because it had more heft!), which the real Grey Fox, a real historical figure, actually used for a while in his train robbing days. The original is in some museum in Canada, near where the movie was filmed.
I don't know when the gunfighter days were, though they certainly weren't confined to the West, but other model guns were also used, including imported revolvers. Likewise cartridge conversions of cap & ball revolvers were popular for a few years, some in big bore rimfire cartridges.