Much more accurate. For nuts and bolts, studs, utility threads, dies are probably sufficiently accurate. Also much easier to do very small threads with a die.
There are features of threads that you may want to control independently, where a die will not allow that. You may want a special pitch for a one time job.....no die practical. You have much, much better control of the PD when single point threading. Major, minor and pitch are all under your control individually with single pointing. Not so with a die. When a die gets dull, yes, you can sharpen it, and some are adjustable to a degree, but no comparison with single pointing.
Main feature to differentiate, to me, is the axial alignment. With a single point tool, it is near dead on accurate as far as concentricity goes. With a die, in my experience, they tend to drift off center, and there is only so much you can do to correct or minimize it.