Warning: This comparison is for superhero comics. Superhero tv series and movies are their own thing that only take the occasional trope from the genre.
The Hero
As much backlash as the genre has faced by puriteens, at heart, superheroes are still all about the might of the self-realized individual, and superheroes are individualists of the highest order. A solo superhero may have contacts and otherwise "supporting cast," but they'll never have -peers-. Other than (perhaps) those closest to them, everyone else sees the superhero differently. Not only that, the hero tends to see themselves differently. Being on a different level in the food-chain as everyone else comes with a different perspective on things, that's why one of the main struggles of the superhero is not losing touch with the people they protect (one that Superman deals with way better than Batman, but that will be stuff for another post).
The shounen anime hero, on the other hand, is educated that only the power of friendship and unity can help him overcome adversity and the monster of the season, so he gets himself a band of merry men, from which he gets backup and emotional support. Also, unlike the superhero (who starts the story already a made person), the shounen anime hero is always a boy out to meet the world and wet behind the ears; as such, he has a mentor/surrogate paternal figure who will help guide him (the shounen anime hero is always a teen, and a male) through the "coming of age" part of his story. The shounen anime hero is always part of a family of which he is spiritually the youngest. In addition, regardless of the amount of power possesed, shounen anime heroes are somehow immune to the power changing their world view (as it would normally happen to anyone else), and will always be the same chuckleheads who can't show up in time for school. Furthermore, this power somehow doesn't alienate those around the shounen anime hero (as it would usually happen in any other case when people finds out their neighbour can erase them from existence with a sneeze).
Beginnings and Narrative Flow
Most if not all superhero comics start In Media Res, with the superhero already fully formed and springing to action in issue #1; "origin stories" are usually told only after issue 2, and in a most abreviated way. The narrartive/marketing model for the superhero comic is a self-contained, episodic one. The reasons for this are twofold: The most immediate one is that, as a product, the superhero must remain recognizable, so the basic premise must not change (just like syndicated shows, the objective is that your potential audience can pick up any random issue and take it from there). The second reason is the same reason why George Lucas started Star Wars with Episode IV and not Episode I: Given the choice, audiences would rather skip straight to the good stuff rather than waiting months/years before being given what they actually paid for (Batman Begins' reception was poorer among the critics than Warner would like to acknowledge).
(20 years training...but you don't want to hear about that)
While shounen anime also follows an (relatively) episodic formula, there are important differences. Your average shounen anime can usually be split in two parts: "Coming of Age" and "Monster of the Season." The first act is a standard, almost cookie-cutter analogy for adolescence, adding some miscelaneous weirdness to the usual "boy meets world". The second part is optional, and is the more familiar, repetitive narrative where a stronger monster appears and lays the smackdown on the hero who then has to "level up" and get a new power in order to beat the enemy. Unlike superhero comics where an episode rarely takes more than three issues, an anime Monster of the Season arc actually takes several months. Once the monster of the season is defeated, repeat the same format with a different villain ad nauseam.
(Just add different villains. Source: vgcats.com)
Crime and Punishment
Superheroes operate outside the law, but still acknowledge the existence of the state and the need to respect it. When not government-sanctioned, superheroes are sometimes persecuted as outlaws, and if they become problematic the state is willing to escalate the conflict (still, even when the superhero could easily overpower law enforcers, they choose not to, just running away instead). In the most extreme cases, world powers have been known to go nuclear once superhumans prove themselves a threat to the establishment (see Kingdom Come).
Shounen anime settings, on the other hand, are basically Westerns; lawless communities where the only effective authority is that of the fastest gun (in this case, the heroes and villains). Law enforcement bodies (i.e police and the army) are, for all practical purposes, non-existant, and the few times they do show up, they're ineffectual at best and openly ridiculed at worst (see Dragonball-Z). Because of the authority of the state being held in contempt, shounen anime heroes are free of the consequences of their actions, just like gunmen in the wild west: Murder, collateral damage, and property damage ranging in the millions of dollars are the order of the day in your average shounen show. This freedom from consequences and contempt for the state also breeds anti-heroes who are considerably less conscientious than their western counterparts. The unshown collateral deaths in your average shounen anime fight would make Frank Castle sick.
(Remember that time the JSDF declared war on
Mazinger-Z for destroying half Tokyo? Yeah, me neither)
Anonimity
Can you imagine how many death threats Robert Mueller (the man leading the current investigation on 45, for those who don't read the news) gets per week? And we're talking about a figure that's so public that is impossible to just disappear (and such incidents have happened, see Hoffa). Now try to take down a Mexican drug cartel while showing your face and having your data available in the phone book and tell me how that works for you and your family. That's why superheroes wear masks, because no good deed goes unpunished.
(One day you're the most beloved lawyer in Hell's Kitchen, and the next you're
sleeping with hobos because your ex sold your secret identity for drug money)
In the case of shounen anime, it's hard to tell how much of this is due to genre conventions and how much to Japan's face-saving-based culture, but shounen anime heroes have no need for secret identities because they have never had to deal with the consequences of stepping on the wrong toes. For some reason, they never have to deal with the possibility of waking up with the head of their significant others next to them, or being sent shoeboxes with their childrens' fingers and genitals, or being fired from their jobs and evicted from their homes (and since it's a western, they don't have to fear incarceration for their multiple, heinous crimes either).
Power Levels
Reed Richards doesn't get smarter or "more elastic" with time. With very few exceptions (like Iron-Man), a superhero gets his superpowers and they mostly stay the same throughout their career. While every (print) decade or so an event may increase the hero's powers, they are given as a straight bump with an in-story explanation (like Captain America getting an indestructible shield during the Secret Wars, and Spider-Man getting the infamous black costume). Most important, a superhero always stays within a same "league" so to speak: No matter how many decades' worth of issues pass, you'll never see Batgirl duking it out with Parallax (not without being butchered at least, see Zero Hour). There are two exceptions to this rule, however, the first one is writers, as writers with favorites then to give specific characters unreasonable boosts as long as they're writing the title. The second exception is characters with "power of plot": Back in the silver age, Superman was plainly as strong as the story needed him to be.
(This was NOT the cover of Action Comics #1,
because this is NOT how the superhero genre works)
Shounen anime, on the other hand, goes full on "videogame logic." Shounen anime series are "zero-to-hero" narratives where the hero is constantly gaining "experience levels" in a steady vertical growth and acquiring new powers whenever a stronger villain appears. The hero starts like an apprentice and ends up like unto the gods, much like a game of Dungeons and Dragons.
In teams, superheroes have peers... alas, peers with egos just as big as theirs. Each superhero is used to be the big fish in the pond, and to do things their way; because of this, in-fighting is common in hero teams, and their greatest weakness is usually their lack of cohesion. Only when they manage to set aside their differences long enough to get things done is that they come victorious. Superhero teams may or may not go for the Five Man Band format, but in either case, the spotlight rotates among team members as much as possible, giving each the chance to save the day regularly (even Hawkeye, and he's the butt of all Avengers' jokes).
(Now picture them trying to decide on where to go for lunch)
Shounen anime presents an interesting contradiction here. You see, while in the theory, the hero needs the friendship and strength of his merry men to overcome adversity, in the practice all that pretty talk goes out of the window about one third into the story, point at which the rest of the casting gets their "experience points" income cut in half so they can get invariably left in the dust by the main protagonist, who is then stated as the one and only valid savior, and the only one who is in any position to face the subsequent monsters of the following seasons. While the merry men still get symbolic promotions, once badass decay settles in, the merry men's fuction in the narrative is reduced to serving as a buffer of human shields so the hero can run the gauntlet set by the monster of the season with as little damage as possible.
(See that name in the title? It's MINE, so stay back, bitches!)
The Role of Women
It's 2017, and I'm still asking WHERE's NATASHA? Much to my dismay, in 2017, the Big Two are still pretty much a boys' club. However, while boys outnumber girls by at least 20 to 1, we have at least a handful of big-league superheroines (see Wonder Woman, Sue Richards, Raven, Jenny Sparks, Jean Grey/Phoenix, Scarlet Witch, Squirrel Girl) to say with confidence that we DO have superheroines that are actually super on their own right. Alas, as already mentioned, the industry is still largely a boys' club, and with the illustrious, aforementioned exceptions, women are not only painfully underrepresented in superhero comics, they are also made purposefully vulnerable. Every superhero goes through dark moments, but heroines are intentionally bereft of the plot armor inherent to male heroes, and are prone to being killed, depowered, and otherwise destroyed with impunity (Women In Refridgerators, anyone?).
(Because nothing says "drama" like killing or maiming a heroine
just to rouse the manly hero into action... NOT)
Now, for women in shounen anime... oh boy, where do I start? While superhero comics have been dragging their feet the last two decades, the industry at least acknowledges we live in different times now (to a degree), whereas shounen anime is unrepentant in its firm belief that we're still in 1950. A lot of people read manga in Japan, and there are genres for almost all demographics... in this case, shounen manga/anime is aimed strictly at a male teen demographic... or rather, a male -juvenile- demographic... a male, juvenile, misogynistic demographic, to be precise: Women in shounen anime are written specifically to be The Chick of the Five Man Band, and are there strictly to be love interests, damsels in distress, or backstage support for the big boys. While a female co-protagonist will always possess a useful skill or even be presented as an apparent badass, once the chips are down, all pretensions of competence will be dropped like a hot potato and she'll be invariably beaten like a chump, relying on the manly man of a protagonist to pull her bacon out of the fire. Even when the story requires the woman to be pivotal to the monster of the season's downfall and even if she actually has the means to do so, it is only after she is
(Oh, sorry Erza, did you really think you were the team's ace?)
Note: While this is a comparison and not a competition, in this area, both sides are almost as bad.
The Hero's Journey
Because of their episodic nature and need to keep an unchanging premise, superhero stories are narratives without a third act: there's no Return and no Freedom to Live, Batman will never hang the cowl. Instead, every time the narrative enters its act 2, something happens and things revert to the second half of act 1 before things reach the point of no return (or sometimes, right after the point of no return, but the farther you take it from there, the more stupid the retcon will look, see One More Day and Maximum Clonage). In the most egregious cases, superheroes live frozen in time: Batman has been 28 years old for almost a century now, and even when his narrative includes 10 years of sidekicks, he is still 28.
(And I want my 20 minutes back)
While the Monster of the Season part of every shounen anime is always the same formula, the Coming of Age part follows Campbell's structure to a Tee. Depending on the series' popularity, however, the return to normalcy may or may not be followed by the Monster of the Season iterations. While shounen anime stories are meant to have an ending, and most do, successful authors risk becoming prisoners of their own success and casted into the hell of churning filler issues and monster of the season iterations until they die (see One Piece).
(There, I just spoiled you the plot of every
shounen anime ever. You're welcome)
Conclusion: Both genres are action oriented, and both are about heroic figures who stand head-and-shoulders above the norm, but each genre has its own unique method to get there, and the results obtained are different for each.
Peace.
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