[Gatofeo]

I've been shooting cap and balls since about 1971. In all that time, I've found a proper-diameter ball to be more accurate than any conical.
Until Jan. 21, 2009.
I had my Uberti-made 1858 Remington .44 out for a day's plinking.
Firing from a benchrest at a measured 20 yards, it consistently put the Lee 200 gr. conical into groups that were 1" vertical and 3/4 wide.
This remains the best group I've shot with any conical bullet, though I have round ball targets that will match it.
Here are the particulars on that remarkable load:

Lee 200 gr. conical cast by me of dead-soft lead.
Home-brew lubricant of Gatofeo No. 1 Bullet Lubricant in bullet grooves.
Goex FFFG black powder - 26 grs. by powder flask.
Remington No. 11 cap, pinched into an elliptical to stay tightly on the nipple.

No greased, felt wad was used under this bullet. Indeed, there wouldn't have been room for one with this much powder, unless you reefed on the loading lever hard, which would have likely distorted the bullet.

Years ago I tried Buffalo Bullets but had little success. Balls were far more accurate.
However, I'll have to try some in this Uberti-made Remington replica. Perhaps this revolver has some special ju-ju.

For the record, this same revolver with .454 inch balls, over 30 grs. of FFFG black powder, and a wool felt wad greased with Gatofeo No. 1 Bullet Lubricant will sometimes put all six balls into a 1" group.
That's from a benchrest, at 25 yards, but not the norm. Those are good days. Most days it will group into 1-1/2 to 2 inches.
My ol' fuzzy eyes don't help matters.

Overall, I'd have to say that balls are more accurate. They are also much easier to get straight in the chamber. That's the key: getting the conical started straight is crucial to accuracy.
The Lee has three driving bands, the lower ones smaller in diameter than those above it, so you can start it straight.
The older designs had no such gradual reduction; starting them straight, and ramming them straight, was usually iffy.
For my purposes, I prefer lead balls over a greased felt wad.

But by all means try conicals in your revolver. If you do, however, fire them against a real target, at a known range, and take your time to load them. Do the same with round balls. This will give you a baseline for comparison.
If you just shoot tin cans and rocks from unknown distances, you'll never be able to learn which is more accurate.