They are most certainly not even close to being the same thing. How far did you go in either show and have you read the books of both, if I might ask? I ask because whilst Rings of Power might reshuffle some of the time line to condense into TV format, altered or invented some backstory for characters (some of which they are apparently legally not allowed to use, such as Annatar being swapped for Halbrand but retaining pretty much the same concept as a background), or even condensed two characters or plotlines together, it still retains a core concept of the books that is undeniably Silmarillion and Lord of the Rings.
Whereas Wheel of Time has changed even the most basic principles of the series, such as how the One Power works, and the Dragon Reborn, and the Aes Sedai, which if anyone here reads the books understands as being crucial parts of the story that once scrapped, changes literally everything. So nothing is similar to the books, except in location name and character name. And beyond that? Rings of Power is enjoyable even if you saw it as stand alone, whereas Wheel of Time is not because it has the cheesiest YA CW show quality in the world, just with a higher budget, and that is all.
Now I can see the complaints Rings of Power has had, but most of it is painfully overblown. I mean, yes, obviously there is a lot different, like with Mithril and Finrod, but changes are expected. It's about how changes are made though, that can effect the way a show is seen. And the Witcher and Wheel of Time? They don't do it well at all. I say all of that as a massive fan of both Middle-Earth and Wheel of Time. There's just way too much wrong with WOT Amazon on top of it just being bad media. I can't even recognize Robert Jordan in that comedic cow dung, where as I can at least still gleam tons of J.R.R. Tolkien (and his son's notes) out of Rings of Power.
I cannot count the number of times I have read The Lord of the Rings, The Hobbit and Children of Hurin, I've read the Silmarillion only twice. I've read the Wheel of Time effectively twice, I re-read the entire series in anticipation of A Memory of Light which I have only read once. As for the shows, I technically watched four episodes of The Rings of Power, although I fell asleep during episodes two and four, and I watched two episodes of The Wheel of Time. I'll note that I've read summaries of the full runtimes of both shows, which, along with this erstwhile essay, is about the maximum amount of time I'm willing to spend on either.
Help me understand what you mean by "core concept". In every sense of the word I see both these particular adaptations as a complete failure on almost every level, and my particular hatred of The Rings of Power stems precisely from its inability to grasp anything resembling a "core concept" of Tolkein's work. It's a lazy and tiresome slog through a visually attractive yet vapid world, devoid of meaning or character beyond the smallest glimmers of something greater which I can only assume the show's creators stumbled upon accidentally. I didn't find The Wheel of Time nearly as offensive purely because I firmly believe that Tolkein's work is probably the most significant contribution to Western literature of the past century, and that in turn colours my expectations for any adaptation of it. But the problems with these two shows are the same, and it's hard to see The Wheel of Time as anything but a testbed for The Rings of Power.
Let me just dispense with the inevitable (and I think I've written this in the Rings of Power thread) and say that in terms of adaptation, I am not nitpicky in the slightest when it comes to matters of adaptation. Peter Jackson's movies are incredible and have set the golden standard for fantasy films and TV series to the point where The Rings of Power continues to unceremoniously ape their general aesthetic - that being said, the films took significant liberties with the actual plot and, in some cases, characterization. You'll see few people lamenting Tom Bombadil's exclusion, but there are plenty of hardcore Lord of the Rings enthusiasts who hate what the movies did to Faramir's character, or to Denethor, or to Aragorn and Elrond.
I am completely fine with all of that, for one very simple reason - they are fantastic films. They were made with care and where liberties were taken with the main story, they were done in a way that made sense with the general pacing and structure of the medium. They made sure to put emphasis where it was needed, and most of all, they kept the major themes of the story at the forefront - heroism, from the ordinary to the extraordinary, a sense of wonder and scale, the sublime, and the presence of real evil, along with its corrupting influence. The plot points may have changed, but the story was the same due to that underlying morality and sensibility, and that is why I consider those movies to be, to date, the best adaptation of Lord of the Rings.
Which brings us to the billion-dollar turd lately plastered, albeit briefly, all over my Amazon packages. The reason why I find these shows to be the same is because they are both cynical products of an industry that seeks to occupy your attention for the brief moment it will take to squeeze the next dollar out of you, and nothing more. I hold no illusions about why Peter Jackson's movies were made, but we now live in a highly-accelerated media landscape where massive corporations vacuum up intellectual properties in order to chase the next trend and the almighty dollar. In this case, Amazon Studios has been relatively up-front in broadcasting their intention to produce the next Game of Thrones, and their ploy in doing so was to snag one of the greatest fantasy properties of all time, and one of its best imitators (at least initially).
As I said, The Wheel of Time was the prototype in this case, and it's hard not to see it that way - it shares the same issues of terrible writing, plot tumors, awful pacing, and a generally lacklustre production that The Rings of Power does. I could not give less of a **** if they change how the One Power works or relatively-minor issues like the Aes Sedai or whatever - I just want them to tell a good story based on the source material. They failed at that while doing what you describe, and this was no more than pure carelessness and poor craftsmanship on the part of the writing team. Why change the way the Dragon works in the story? For
no reason, other than a cheap mystery-box plot arc for a few episodes. Why change Rand and Egwene's relationship? For some cheap sex scenes and a manufactured romantic plot tumor. It's short-term thinking from the creators for the simple reason that they don't care about the plot or even the long-term viability of the story nearly as much as you do - they only care about whatever they can do to keep as broad an audience as possible "engaged" so that they can in turn consume the next bit of "content".
And what of The Rings of Power? The one credit I'll give the show is that it resisted the urge to include the now-mandatory lurid sexual content found in its peers. As for the rest, it's very much the same as The Wheel of Time. As an example, episode one's interaction between Galadriel and Gil-Galad is a Middle-Earth'ed version of a scene from a cut-rate cop drama, where Galadriel is the loose cannon and Gil-Galad's asking for her badge and gun and shipping her off to Valinor. This is offensive on multiple levels - beyond the **** writing in general, it cheapens our conception of Valinor and the elves. The show is full of this nonsense - script elements and plot beats Frankensteined together from past popular shows and lazily thrown together, throwing a mountain of **** at the wall and hoping some of it will stick and generate "engagement". The persistent presence of, again, cheap mystery-box plot points serves to illustrate both just how little the writing team evidently cares about what they're creating as well as how little they care about the long-term viability of the project as a whole. The whole Harfoot plot essentially boils down to "it was Gandalf the whole time", something any viewer with even a casual interest in Lord of the Rings probably guessed to begin with, but which was not only conceived of as a good idea for a central plot thread but also strung along as an actual mystery for the entirety of the season, revealing that he "IS GOOD" to absolutely nobody's surprise. What is the point of this plot thread existing? Why does it exist to begin with? Simply because it crams a cheap mystery into the show's opening act, unstealthily sneaks a pointed connection to something that just reminds you that Peter Jackson's far better movies still exist, and, importantly, connects to the other big mystery that unfolds over the season - where's Sauron?
That one in particular is deplorable for the typical reduction of a grand-scale conflict of good and evil to petty interpersonal drama. Galadriel hates Sauron because he murdered her brother; Sauron, in turn, is content, apparently, to chill on his vacatipn yacht until Galadriel jumps into the middle of the ocean and happens to find him, and is so annoying that she reminds him why he wanted to enslave the world again. She subtly falls for not-Aragorn (and I feel like we were one board of directors meeting away from getting a sex scene here) because he, too, is a loose cannon cop until she realizes it was actually Sauron, and the real evil was HER! Oh no! I honestly have no words for how bad this plot is. I could go on and on about other stuff, like Trump's Numenor, the IT WAS MORDOR ALL ALONG, the lack of scale, the laughable attempt at what they were trying to do with Adar, but hopefully I've gotten my point across.
Cheap is the word I would use to describe The Rings of Power - for the immense amount of money that went into its creation, it thinks remarkably little of itself as a work of art, because it isn't. It is merely "content", it knows this, and you can even trace the point where Amazon turned off the money valve to generate interest and "engagement" from the various bought-and-paid-for publications. It is poorly-written, disastrously-plotted, and made in the sincerest spirit of mediocrity. Its existence offends me, not because of its quality as a Tolkein adaptation, a criticism I was more than willing to leave at the door, but because it is an utterly inferior cultural product masquerading as something with greater pretensions.
It fails completely even if it were an original setting with original characters. That you claim to enjoy it and not The Wheel of Time is simply mind-boggling to me. I fail to understand this on any level. What do you like about it? Why? Try to describe the story of the show without any specific reference to characters or events. If you're having a hard time, it's not a good story.