What's more accurate in a .58????
When I say, "ball" for Enfields, I'm talking about ".58 caliber expanding ball" ammunition. This is what the "Minnie balls" were called during the civil war. They are conical bullets with a hollow base that expands when the charge goes off, causing the bullet to take up the rifling.
Also used were British Enfield cartridges that had smooth-sided expanding balls that were designed to be shot with the paper of the cartridge still around the bullet, making essentially a paper-patched bullet. It was still an expanding ball kind of ammunition though. It just had no lube grooves because the paper cartridge itself had the bullet end dipped in lube so the paper took up the lube.
I'm sure you could shoot a patched round ball in an Enfield, but I have no idea what to expect from it.
Here is a nice article on period ammo: