Unfortunately, the animation adaption is horrendous.
The show was basically left hanging out to dry, by essentially outsourced it oversea to China, who didn't do a very good job at bringing it to life. The art of the comic is great, but not at the level that needed massive budget to animate. But, they need to completely capture the original material quality character's illustration. They couldn't even do that. The characters illustration doesn't translate well despite decent original design. The background is lifeless, bloodless, as if I was sent back to the early, mid 2000s animation quality. The background back then was at least stylistically hand drawn, with brush and and all. The worst sin of the animation, to me, is the awkward mouth movement. I suspect most of that was due to the Chinese animation studio having very little experience with how the mouth should move because they don't speak Japanese, so they relegated to just adding open and close. The key animations might have been done in Japan, then shipped to China for frames in between and colouring. The one part that the Chinese did well seem to be the "action" parts, such as Hime falling from the platform, jumping, galloping and characters flying around, kicking. This studio could do a much better job at animating a dumb, generic shounen action show than be given a really subtle CGDCT.
The sound quality is nothing to write home about. The music is largely forgettable and the voice acting is capable, albeit adding little to the show, due to the nature of it and the distance between where it was animated and where the VAs are. A good counter example is Konosuba, where the animation became much more engrossed and inspired by the voice actors efforts, turning a relatively poorly animated show into a gem, as the studio figured out where to focus their efforts into.
I don't think there's much to be said about the story, because I advice against watching the show and recommend just picking up the comic. It was adapted without changing very much, which is both good and bad. What's great has been reflected by other reviews, who praised the show for world building and adding layers to CGDCT. I won't go onto too much details, people can already take it in.
There's an obsession with "policing" equality, making sure nobody is offending anybody. Yet, for all of the policing, there were still huge distrust of outsiders, particularly towards the 2 reptiles races. The funny Nazi part also alludes to the fact that, even if humanity all look the same, discrimination will still happen, we would just find things different about ourselves to fight over. You can explore more of that topic by reading about Rwandan genocide, where the word genocide met an unfortunate circumstance. Genos indicates race, people, yet the Tutsi and Hutu are basically physically indistinguishable, leading to many mistaken victims and survivors due to the killers not being able to tell them apart. That's great food for thought, if one is in the mood for such. Else, the viewer can continue enjoying cute girls doing cute things being poorly animated.
Another part of CGDCT being twisted, not to the point of deconstruction, is slice of life, CGDCT can have a lot of depths, that can be explored, yet, they are not being used for drama. This is in contrast to the great Maeda's modus operandi. There are many notable parts, such as Hime the centaur's red hair origin, or the class president's family circumstances. The class president is a notable character with a lot of shocking character. Her family is cute, but she's head strong, mature, bossy and motherly, not just because she's a CGDCT character, "perfect class president" type; but she has to be this way because her father is essentially a delusional deadbeat dad, her mother passed away living a weak child, and she has to take care of a bunch of noisy, spoiled and energetic little sisters. The comic frequently contrasted her family circumstances to Hime, who's spoiled but nice, because she was brought up in a loving family. Yet, these details always take a backseat to the cute girls doing cute things, because at the end of the day, it is still slice of life, and not served as the basis for drama and shock moment like what Maeda does.
That's just a taste of what's to come in the comic, which had a lot more interesting details about the world and the author's world view. I highly recommend that. The animation, not so much. Centaur no Nayami the animation is a train wreck, and should be avoided if possible. There's a lot of good in the story, but that's due to the original work. The animation added essentially no value to the experience.
