Balls are almost always more accurate than conical bullets, because it's often difficult to get a conical bullet started perfectly straight into the chamber.
An exception may be Lee's conical bullet, which is designed with progressively larger bearing bands from the base forward. The bottom band slips into the chamber easily, to help align the bullet. The second band is only slightly larger, to help even more with alignment. The curvature of the bullet nose, just before the topmost grease groove, is oversized.
Having two guiding bands and then a fairly wide bearing band near the nose helps keep the bullet straight during seating.
In more than 40 years of shooting cap and ball revolvers, the Lee design is the only conical design I've found that can equal, or nearly equal, a ball.
Use a ball of .454 or .457 inch diameter. The older loading manuals suggested .451" years ago, but I gave up on that size about 20 years ago. The larger balls are more accurate.
I believe I was the first to postulate that the larger ball created a wider bearing band when seated, for the rifling to grip. I never saw it mentioned anywhere until I began posting my theory on the internet about 2000. I have every American Rifleman printed since 1929, a complete set, and the idea is not in there. Nor is it in any black powder books dating back to the 1960s.
At least, that's my theory. You might be able to show a correlation between larger balls, and postulate that the wider bearing band is responsible, but just how you'd prove it is questionable. High speed photography (a subject I'm familiar with) wouldn't show it.
I guess it will remain unproven, but observed.
