I certainly haven't seen Rowling talk about this but:
One Answer suggests that it is possible but is it really so? If it is it's still very different (other than the part that each have some of their creator in them). You're forgetting some important things about the One Ring and the Horcruxes. I know the question actually points out that it's not exactly the same but I would like to explain how and why this is the case (as well as point out some interesting points that maybe haven't been - and might have - thought of).
A Horcrux contains a part of the soul so that if the creator were to die they could not die because there is still part of their soul living in another object. They could return - as Voldemort does. At this point it seems like the One Ring is similar, doesn't it? As long as the One Ring survives so too does Sauron (but Sauron never dies). But the similarities end there; there are significant differences:
When all the Horcruxes are destroyed Voldemort is still a formidable foe; Dumbledore says this directly in HBP:
Harry sat in thought for a moment, then asked, 'So if all of his Horcruxes are destroyed, Voldemort could be killed?'
'Yes, I think so,' said Dumbledore. 'Without his Horcruxes, Voldemort will be a mortal man with a maimed and diminished soul. Never forget, though, that while his soul may be damaged beyond repair, his brain and his magical powers remain intact. It will take uncommon skill and power to kill a wizard like Voldemort even without his Horcruxes.'
Yes quite a bit of Sauron is in the One Ring but what happens when the One Ring is destroyed? Is Sauron killed?
In fact when the One Ring is destroyed Sauron is not killed but he is diminished to an impotent shadow that could never threaten Middle-earth again (see next paragraph too). But what happens if all of Voldemort's Horcruxes are destroyed? Not only is he still alive but he still has exceptional magic (see above quote); he's mortal once more but he's still a powerful wizard. He also has his armies (and he still has his body).
Actually Sauron never is 'killed': when he caused Númenor to drown he did not 'die': he could never be fair again but he was still a formidable foe (though not immediately). Not when Elendil &co defeated Sauron (followed by Isildur cutting the Ring off his finger) did he 'die'; he lost his shape again but he returns in full form once more (with the Black Hand having only four fingers).
Critically there is this: if Horcruxes were the same idea then one of the following would hold true:
- When all of Voldemort's Horcruxes were destroyed he would become impotent and never be able to threaten anyone again. In addition his Death Eaters would all be confused (I use the word 'confused' very loosely here). The latter doesn't happen (and here it might be more like they claim they were under the Imperius Curse rather than freely giving themselves up)
- When the One Ring is destroyed Sauron and all his armies would still be a real danger to everyone. Is that how it ends? Well some of his armies were still dangerous but they were defeated; others gave themselves up. But either way Barad-dûr was destroyed, his Nazgûl were no longer a threat and Sauron could never threaten Middle-earth again.
But do either of those scenarios happen? No. When Voldemort's Horcruxes are destroyed he is mortal and thus at risk of death. When he is killed some who were truly under the Imperius Curse had control of themselves again; and yes you could argue this about when Sauron is defeated. But when Voldemort's Horcruxes are destroyed he still isn't defeated; when the One Ring is destroyed Sauron IS.
What might be interesting to point out though is that some of the Horcruxes had an influence on those who were in possession of them (or 'used' them where use could be writing in or wearing). These were negative influences though. Still having the One Ring also had influences but quite different. Does that make them more alike? I think that's a matter of opinion; personally I don't see it that way but it's certainly a similarity of sort.