I am a real fan of the cap and ball revolver and I have had .31, .36 and .44. of both Colt and Remington styles. I have never been able to get a colt repro to shoot better than a paper plate at 25 yds. The best I ever did with a "true" Remington style was a cheap brass framed .36 I bought at a going out of business sale at a discount chain store. The trigger pull was terrible, but I could hold a 4 inch group at 25 yds. When I practice with my Ruger Old Army, I have even shot 2 inch five shot groups at 25 yds. (with a perc. muzzleloader pistol, I once shot a 1.25 inch group at 25yds, in competition)
I firmly believe it has more to do with the pistol than the caliber. If Ruger made a .36, I'd buy it. If they made any other caliber, I'd have to buy one.
A .36 has less recoil, assuming a similar weight pistol, and less report to throw the shooter off, but that is a matter that is overcome by practice no matter how big or small the bore. If you shoot and practice alot, a .36 runs about half the cost for shooting supplies and powder.
I once competed regularly against a fella that swore by his Rogers and Spencer as the very most accurate. But he also took his pistol to a nationally known pistol expert to have it tuned, smoothed and reworked. He probably spent $150 for the gun and another $500 for the gun smith work. He could shoot cloverleafs all day.