Theres an entire genre for it, seinen. Serial Experiments Lain, Ergo Proxy, Ghost in the Shell, Cowboy Bebop, etc

you can't go looking for a one to one comparison. the equivalent is going to be mostly well animated adaptations of successful seinen (and some shonen or shoujo or josei that fits the bill) manga. even if they aren't as grounded as breaking bad, they'll still hit that spot comparatively. this is where erased and monster are. things like the recent chainsaw man anime might count, as well as upcoming anime such as dungeon meshi and pluto (based on a manga by the guy who did monster). older examples might include mushishi, space brothers, ghost in the shell: sac, possibly kaiji. jojo part 7 might actually qualify (though none of the previous ones would)

original anime are trickier but some that come to mind would be things like oddtaxi (which i think fits all your criteria), violet evergarden, paranoia agent, maybe a psycho-pass or anohana. if you're willing to get a little more out there you could include more experimental stuff like the works of ikuhara, or lain or princess tutu. and some big franchise stuff like woman called fujiko mine or gundams like 0080 or ibo might qualify as well

i haven't watched everything i mentioned here, but my understanding is that they're all relatively sober, serious works that have thematic content not normally seen in your demon slayers or isekai of the seasons. most of them are fairly melancholic in tone, and though almost all are scifi or fantasy they take a somewhat grounded approach to the subject matter and aren't power fantasies. (the ones i mentioned as being experimental might not fit this, but they're good enough i needed to mention them).

For both dark and realistic, I can't think of too many off the top of my head. Besides Monster and OddTaxi, I'd say a lot of Satoshi Kon's works could count.

If you're willing to get into just a little bit of fantasy/sci fi tech then there's quite a bit.

Shinsekai Yori, Psycho Pass, Lain, Tokyo Magnitude 8.0, etc.

Does Puella Magi Madoka Magica count?

There's three big distinctions between American Prestige TV and Japanese Anime that I've noticed (other than the "one's animated" bit).

• Younger protagonists/antagonists: There's a Japanese fascination with the idea of a protege or savant that dominates even the most serious shows. Whether you're an ultra-ace pilot, genius detective, or (most commonly) a primary school student who just happens to be smarter than everyone three times their age, the anime lionizes young people who behave like adults. As a kind-of knock on effect, this results in a fair amount of graphic depictions of children - violence, nudity, and other situations that a Prestige TV show in the US simply isn't going to want to touch.

• A fixation on rivalries: US Prestige TV tends to hone in on existential or obscured threats. The ultimate antagonists of shows like Sopranos and The Americans are rarely present on the screen. Whether they are crime bosses or government officials, they tend to operate at a high level with the protagonists operating as pawns in a much bigger game. Even big political shows like GoT and House of Cards tend to get away from the primary antagonists and focus on the daily life of the protagonists, with major conflicts coming suddenly and at the tail end of a season. Compare that to anime, where the major rivals are a regular presence on screen and are keenly aware of the protagonists as the most important players in any conspiracy or conflict. There amount and significance of dialog between Walter White and his wife and son simply wouldn't exist in anime. That time would be spent on White and his current drug-dealing arch rival, trading verbal barbs in an escalating game of cat-and-mouse.

• Gaming: Anime fucking loves games. Maybe that means a heads-up tournament a la DBZ or Naruto. Maybe that comes in the form of an elaborate game of riddles or some obtuse chess match, as in Terror in Resonance or Death Note. This regularly leaks into the live-action dramas as well, with Squid Game being the most obvious recent example. Episodes almost always involve some kind of very explicitly stated challenge with rules that are somehow rigidly enforced. These are presented to the audience as an invitation to solve at home (or simply to marvel at, with the implicit assumption that you're a bunch of dumb-dumbs who can't run around an airport playing chess on a mental board). Prestige TV, by contrast, will regularly hand wave the How of a particular scheme or add enough professionalized jargon so as to make it inscrutable. You're not supposed to think too hard about the Magic Island from Lost or the mechanisms for accruing celebrity in Atlanta. The focus tends to be on social relationships, decisions, and betrayals, as well as the hedonism that drives people to acts of increasing desperation.

I'm sure I could come up with more. But in every case, it does feel like the American Prestige show is trying to empathize with a much older age group of "normals" while the East Asian high profile cartoons are constantly appealing to late-teen/early-20 something folks that empathize with feeling Special. Asians are focused on the upward climb while Americans are entranced by the fall.

I don't think its a coincidence that anime also has a habit of resonating with American kids in GT/Honors classes or with some other self-described sense of elevated ego or purpose. Meanwhile, Prestige shows tend to play well with folks who feel run down, who feel they've missed their big shot, and people who like rooting for the dumb guy.

Samurai Champloo and Aoi Bungaku are two of the only animes I like for this reason. The latter has a great adaptation of No Longer Human, one of their best modern novels.

deleted by creator

Gundam.

Definitely Monster, as you said

Maybe Logh? I don't usually think of sci-fi as prestige TV. Similarly, Baccano! kinda hits some of your points but is modern urban fantasy.

I haven't seen it in years and don't really remember the plot, but maybe Michiko and Hatchin would fit the bill. Also Moribito could fit, which is set in feudal times but very light fantasy element if any.

How about Leader, the Chiname about Marx & Engels? Perhaps production value too low

ODDTAXI (This is the one you're looking for)

The Rose of Versailles (This one also has good politics near the end)

Cowboy Bebop

The Tatami Galaxy

Ping Pong the Animation

Neon Genesis Evangelion (Grounded? No, but I think its directing style is more film-like than most other anime)

Kaiji

Akagi

Death Note (maybe)

Steins;Gate (maybe)

Sonny Boy (maaaaaybe)

That's what I got, idk if all of them fit the category exactly. Odd Taxi definitely feels the most "TV-like".