Most anime these days aren't completely new IPs. There is a good number that is, of course, but most of them tend to be adaptations of manga (which were also likely adaptations of a light novel). And, as many of these mangas get adapted, there are aspects of the story, fan-favorite moments, or even just the style of the series that are lost in translation.
This isn't always a bad thing and usually isn't intentional, but it does happen a lot. To prove this point, let's look at some examples of series that were adapted, and yet ultimately their manga iteration ended up being the best way to experience them.
8 Gate: Thus The JSDF Fought There
First up is maybe a controversial pick, it's Gate - Thus the JSDF Fought There. This story details the war, relations, and ever-expanding story between Japan and this magical fantasy world that suddenly had a gate open up in this alternate version of Earth one day.
Now, there are actually three ways to experience this story, a light novel, manga, and anime. The LN is widely accepted as the best method of enjoying it, but the manga is a close second. The Gate anime isn't bad by any means, it just makes a lot of changes. The art style is more industry-standard, the politics are played down a lot, and the supporting cast has less screen time.
7 The Faraway Paladin
This one might be more of a niche pick but The Faraway Paladin has to be on here. Again, like Gate, the anime adaptation of this story got was good and did its best to tell William's story without losing too much in translation.
But, the art in the original manga is just so stellar, and it's used to enhance the storytelling in a lot of ways. Additionally, the emotional highs hit harder in the manga thanks to the detailed linework, the world William explores is expanded upon more in-depth, and the interpersonal moments between characters just feel more natural.
6 By the Grace Of The Gods
By the Grace of the Gods may be one of the comfiest, almost slice-of-life-esque stories out there for fans of the isekai genre. The primary reason for this is that the main character, Ryoma Takebayashi, was an almost-40-year-old man who had an exceedingly tough time. He came from a tough household with an abusive father, was constantly mistreated by the people around him, and never got to relax at all. Now, in his second isekai life, Ryoma is living a much happier life and all of the skills he picked up on Earth have now translated to his new body.
From there, Ryoma quickly learns that he loves taming monsters, slimes in particular, and quickly becomes the forefront genius on it, carving out a life for himself in the process. Let's be real, fans of BtGotG are happy it even got an anime in the first place, but that said, the anime's story structure is a bit all over the place and it doesn't include as much of the original source material as people probably would have preferred.
5 The Rising Of The Shield Hero
The Rising of the Shield Hero, like a lot of the entries on here, is a story that people can experience in a multitude of different mediums. There's the original web novel, then the published light novel, then the manga series, and now the anime, all telling the story of Iwatani's adventurers as the persecuted Hero of the Shield. Now, the anime for Shield Hero is fantastic, especially the first season with its amazing opening.
But, it seems to be trying to incorporate narrative structures from all three other versions of the story and this is causing a lot of fans to feel like the anime story is messy and confusing. That said, it's still one of the better isekai anime out there, especially for DanMachi fans.
4 Saga Of Tanya The Evil
This next entry is actually very similar in its reasoning as Gate was, and it's Youjo Senki. Better known as Saga of Tanya the Evil, this story started as a web novel, was published as a light novel, released as a manga series, got an anime adaptation, and even had its own anime movie made as well. So, it's safe to say this series is pretty popular.
And, like Gate, there are different reasons for each medium as to why people should experience Tanya's story that way. The original light novel is by far the most expansive version, as it has all of Tanya's inner monologues and goes much more into the politics of the story. The manga is a bit less word-heavy compared to the LN, but also has more action. And finally, the anime is the most action-heavy by far and has a massive change in the art style from both the LN and manga, but is the least-liked version by fans who read the source material.
3 Arifureta: From Commonplace To World's Strongest
Arifureta is absolutely one of those isekai stories that fall under the label of "power fantasy" where the main character starts off exceedingly weak and then through some unfortunate circumstance works hard enough to become unbelievably stronger than anyone who ever treated him wrong. And, to be fair, Arifureta does innovate on this concept in a lot of ways as Hajime's (the protagonist) progression from basically dead at the bottom of a dungeon to tsundere trenchcoat-wearing gun-toting badass is slow and steady at first.
This story did get an anime adaptation, and it was relatively faithful to the source material. But, it quickly became clear how fast they were rushing through the story to try and cover it all as fast as possible, and there were a lot of corners cut both visually and in the writing that didn't need to be.
2 How A Realist Hero Rebuilt The Kingdom
Moving on to one of the more egregious examples of an anime that cuts a lot from its source material it's the anime adaptation of How a Realist Hero Rebuilt the Kingdom. This story is a pretty unique take on the isekai concept, as instead of putting the earthling who was transported to this fantasy world to work as a hero, Kazuya Souma is instead given the title of Elfrieden's King. As soon as he shows up, the king abdicates the throne to him and Souma must now save this failing kingdom from all their economical, political, and general nightmares.
The original light novel for Souma's journey as a king is incredibly in-depth and does a lot of world-building. Then, the manga adaptation kept a lot of that material while also adding this storybook-esque style to all the characters. But sadly, the anime adaptation, while well-intentioned, completely ruined the art style of the manga and rushed the story along trying to adapt as much as possible in the shortest number of episodes.
1 Black Summoner
Finally let's end things on one of the more recent examples, Black Summoner. This isekai story was unique in a way that was different from most, as it almost doesn't even qualify as an isekai. Yes, Kelvin is from Earth and was transported to this new world with levels, classes, and adventurers. But, he traded all his memories of his past life for extra skill points so that he may summon his "love-at-first-sight" that much sooner, the Goddess of Reincarnation Melfina. So, in a sense, he literally can't follow many of the tropes other isekai stories do.
The manga adaptation for this series is fantastic, as the art is unique, very readable, and does a lot to emphasize the action or even emphasize just Kelvin's devilish smile. But the anime adaptation is a different story. For the most part, it's pretty passable as it only slightly changes the art style and keeps to the same story for the majority of it. But, it's the combination of a bunch of smaller factors such as Kelvin's smile being much less memorable, the action using a lot of obvious CG (especially the fight between the soon-to-be-friends Kelvin and Gerard), and some skipped content that makes it so that the manga or even the light novel are the better options for enjoying this story.