It's kind of surprising to me how much these two fandoms don't overlap. I tried to make a variation on the Dio meme that was about the Captain Atom/Monarch fiasco and nobody got it. Plenty of people who are deep into one of those rabbit holes is familiar with the most well known Normie examples of the other, but that's about it.
As someone who's DC fandom is far older then my Anime fandom, and yet has come to now view Anime as what I'm more of a fan of then anything else. I'm perhaps uniquely qualified to try and identify how to reel others in.
The Anime that are most explicitly made to evoke Western Superhero aesthetics, stuff like One Punch Man and My Hero Academia, actually don't appeal to me. They're just Battle Shonen (one of my least favorite Anime genres) with more Capes and Masks.
The Magical Girl Warrior Subgenre was influenced by Superhero comics in a very particular way. If you're of the opinion that Wonder Woman was only great in the Marston era and everything since Denny O'Neil has been a hollow shell, then Sailor Moon or Wedding Peach might be exactly what you've been looking for. But I know there will be others that won't be able to get into that genre, at least not without being phased into the Bishoujo first. So my focus today shall be more Seinen.
For me the show that wasn't my first Anime but the one that really felt like a unique and interesting approach to tropes and ideas I was already into from my prior Nerdiness was Code Geass. There was a thread on IMDB once about comparing Lelouch to Simon Bolivar, I wasn't as familiar with that piece of history as I am now (which is still not a whole lot), but I left a comment on how I liked to compare Lelouch to Alexander The Great and Paul Atredes and Batman and Spiderman and Ozymandias, but there was also overlap with what I loved about the Star Wars Prequels. Later when I started getting into Paul Feval his John Devil was added to that list. The show also had Shakespearian qualities in some of it's dialogue exchanges that are more subtle then literal Iambic Pentameter.
But one thing I kept noticing when I rewatched the show earlier this year was how many Anime tropes and clichés it had that I wasn't prepared to recognize as such when I first watched it. This was my first Absurdly Powerful Student Council, my first School Festival and even my first taste of some of Anime's special kind of degeneracy (wasn't my first sample of Yuri though). It introduced me to those things but not in doses unbearable for someone who'd prefer not to have them.
Thing about Code Geass is while it was great for me others might need something even less perverted.
Death Note is a show I watched because it's lead was often compared to Lelouch. The show provides a great Holmes vs Moriarty style battle of wits, for a certain kind of Comic Book Nerd it's exactly what they want. But I'm more looking for what will appeal to those who's tastes are less dark.
For people like Linkara, I really recommend starting with A Certain Scientific Railgun (but skip the second episode on your first watch) and then the show it spun off from A Certain Magical Index. Railgun is a Seinen show that could easily pass for Shoujo, and at times I feel like it has an appeal that is very similar to why Teen Titans is my favorite DC franchise yet I can't really explain why.
Railgun is better then Index at least in their Anime versions for a number of reasons. The main thing that makes it a better entry point for Normies is having none of Index's egregious fanservice, only the most G rated allusions to that aspect of the culture.
But also during Railgun T especially it proves to be a show where the battles actually put thought into making interesting use of the characters' various powers and abilities.
Once you are into this universe, you probably will want to check out Index and Accelerator eventually, because there are aspects of the universe only those shows can get into.
Update January 2022: I wish I'd watched some Detective Conan before I wrote this, it's a show I was aware of but it's different then I expected. Some of the shows above involve dual identified but how they function is a bit different. There are occasional episodes of Detective Conan where Ran is very much on to Conan being Shinichi, and they way they play out constantly reminded me Lois Lane in the first act of Superman II.
Update Again: Months later and Conan is still holding up, it combines the Teen Drama Superhero antics of Spiderman with the Gadget wielding non leathal Detective antics of Batman. And in time it develops an interesting cast of recurring villains.
Also magic Kaito which it spun off from is good too, it's Manga is older but the Anime is newer.
The movies are often more action orientated then the show, and have on average gotten less cleverly written as time as gone on, but I find mostly all of them, even the dumbest Conan film is smarter then any MCU film.
Update August 31st 2024: I also now want to add Durarara! to the list, it has a lot of qualities that remind me of those DC Comics where you just kind of hang out in the DC Universe.
