There’s no way to rank them in power.
The functions of Horcruxes and enchanted portraits are entirely different, so there’s no logical way to rank them in a hierarchy of which is more powerful. They’re inherently different in what their purpose is.
Horcruxes tie their creator’s soul to earth.
Creating a Horcrux requires committing murder to split the soul, and once the soul piece is encased in an external object, the wizard who created the Horcrux cannot die because their soul is tied to life.
“Well, you split your soul, you see,’ said Slughorn, ‘and hide part of it in an object outside the body. Then, even if one’s body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged. But, of course, existence in such a form …”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
They keep the wizards that create them tied to earth, ensuring that their soul remains alive, giving them immortality. Their bodies may die but their souls will remain and they can create new bodies.
Paintings mimic their subject’s personality.
Though they have varying levels of their subjects’ personalities, paintings aren’t truly their subjects - they’re just an imprint of them. They also do nothing to keep their subject alive, their subjects are all dead.
All the paintings we have seen at Hogwarts are of dead people. They seem to be living through their portraits. How is this so? If there was a painting of Harry’s parents, would he be able to obtain advice from them?
That is a very good question. They are all of dead people; they are not as fully realised as ghosts, as you have probably noticed. The place where you see them really talk is in Dumbledore’s office, primarily; the idea is that the previous headmasters and headmistresses leave behind a faint imprint of themselves. They leave their aura, almost, in the office and they can give some counsel to the present occupant, but it is not like being a ghost. They repeat catchphrases, almost. The portrait of Sirius’ mother is not a very 3D personality; she is not very fully realised. She repeats catchphrases that she had when she was alive. If Harry had a portrait of his parents it would not help him a great deal. If he could meet them as ghosts, that would be a much more meaningful interaction, but as Nick explained at the end of Phoenix—I am straying into dangerous territory, but I think you probably know what he explained—there are some people who would not come back as ghosts because they are unafraid, or less afraid, of death.
- Edinburgh Book Festival (August 15, 2004)
There’s no Dark magic required in creating a portrait, nor murder, but they don’t offer their subjects any additional life either.