Remove curse can remove all curses on an object or a creature. If the target is a creature, you must make a caster level check (1d20 + caster level) against the DC of each curse affecting the target. Success means that the curse is removed. Remove curse does not remove the curse from a cursed shield, weapon, or suit of armor, although a successful caster level check enables the creature afflicted with any such cursed item to remove and get rid of it.
The first sentence says it can remove all curses from an object or creature. Later in the paragraph it gives the exception of cursed shields, weapons, or suits of armor don't have the curse removed, but they are able to be taken off and be gotten rid of.
So a ring, necklace, or other cursed Wondrous Item that isn't a shield, weapon or suit of armor can have its curse completely removed from a casting of Remove Curse? If so, why does Break Enchantment, an even more powerful form of the spell, only allow things to be taken off or gotten rid of, and not also completely "remove all curses from an object?"