We do, at the very least, know why Gandalf's magic works. The universe was sung into being, and Gandalf is a divine being who can participate in that song. We know where his magic comes from. We know it's divine in origin.
We don't know where Harry's magic comes from. Were wizard blessed by a god? Is it a magic gene? Is it fueled by intelligence, or imagination? There are no answers.
Take horcruxes vs the one ring. One is clearly a second rate copy of the other. But the one ring has a clear limitation for Sauron: It holds most of his power, and if it's destroyed, he can be defeated. What limitation do horcruxes have for Voldemort? He has to split his soul into parts. What does that mean practically? Nothing. It's not a limitation, it's just a reason the good guys don't use it. From the council of Elrond, we know the rules of the one ring, and we know how to use them to solve a problem. Sanderson's first law. Its limitation for Sauron is more interesting than its power for Sauron. Its limitation for the Fellowship is more interesting than its power for the Fellowship. Sanderson's second law.
Looking evil isn't a limitation, it's flavour text. It doesn't affect the story, it just gives us vibes. If there's one thing Rowling is good at, it's writing flavour text to convey vibes. But there's no plot in that limitation. Horcruxes break Sanderson's second law, and that's why they're not as interesting as the One Ring. The One Ring puts challenges in front of every character who interacts with it: Sauron, Isildur, Elrond, Bilbo, Gandalf, Frodo, Gollum, Galadriel, even Samwise. It promises all of them something they want, and takes a price from every one, changing the course of the story many times. Samwise is the least affected, but it still takes away something he loves; his best friend.
Horcruxes do four things: they kill Dumbledore, give Harry a quest, make Ron grumpy, and ex machina the deus. Bringing Voldy back and manifesting Riddle don't count because those are retcons, and we're talking about writing processes.
Two of those things they do are just because they're a macguffin. Literally anything the characters want could have been substituted. Ron grumpy is, again, flavour text. The Deus ex Machina is the one interesting thing they do to change the story.