It would be highly dependent on how you define and measure "stopping power" and that is a topic for which there seems to be little, if any, consensus. If you take the velocity, weight, and bullet diameter of a .36 caliber round ball fired from a Colt 1851 Navy revolver, you're pretty close to that of a .380 ACP so that's probably where I'd start. 9mm uses the same diameter bullet as a .380, but it's heavier and at higher velocity so you're probably not going to match it with a .36 round ball. You might get your weight and velocity fairly close to a 147 gr subsonic 9mm by going to something like a .44 caliber round ball from a Colt 1860 Army, but the diameters are obviously different as is the bullet construction. In order to match a 9mm JHP when bullet expansion is taken into account, I would think you'd probably have to use a .44 from something like a Dragoon or Walker which can achieve a higher velocity and be using a very soft round ball made of pure lead, and even then you might not get there because the .44 RB may still not deform to the same diameter as the 9mm JHP.
Now if you start taking kinetic energy into the equation, things will get more complicated still as something like a Walker can push a round ball of about 140 gr to 1200+ fps with a full 60 gr load which is getting into .357 Magnum velocity, weight, and energy. That being said, the .44 RB will likely deform little, if any, in an erect biped and is more likely to simply generate through-and-through penetration as compared to a modern JHP.
Basically, no matter which way you look at it, you're going to have to go to something like a Dragoon or Walker to even hope to be comparable to a modern JHP in 9mm or bigger. The size of the gun you'd have to use would make it rather impractical as Walkers and Dragoons, even in the 1800's, were considered too large to be practical to carry on one's person (they were often referred to as "horse pistols" because they were usually carried in holsters on one's saddle). You simply aren't going to match the weight, diameter, velocity, and expansion of a 9mm JHP with a cap-and-ball "belt pistol" like Colt Navy, Colt Army, or Remington New Army and you won't even be in the same ballpark with something like a .31 Colt 1849 Pocket revolver. Round Balls simply aren't a very efficient bullet design and that's why they were replaced with things like conical bullets and Minnie Balls once those designs became available and practical. Unless there's nothing more modern available, there's really no good reason to choose a percussion revolver with round balls over a more modern firearm with modern ammunition.
