Either it's deliberate or coincidental, the fact is the following shows are comparable to an uncanny degree.
*Ordered chronologically through Batman*
The late 60's
Essentially, amidst the "Adam West Era" of superhero television, these are what we, in the modern era, deem campy, cheesy, and the like. The sound effects, the action, the dialogue, the acting and the limited animation cemented that perception. Sixties' Spider-man retains relevance because the internet community made memes.
The late 70's / early 80's
Aside from being another set of shows beyond my time, both are cosmetic updates of their respective 60's predecessors. After managing to catch a clip or an ep, that might be where the parallels end. Spider-man '81 got more serious in tone, ex. Wizard isn't that hammy of a villain and does have a sensible scheme despite the looney endgame. The emotional drama is somewhat more believable with apt stakes. The New Adventures of Batman added a wacky side character and had a very telling production budget. Spider-man '81, on the other hand, had more animation and characters' faces could at least be more expressive transitioning between different moods.
*Spider-Woman had her own show at this time. There is no equivalent in Batman's adapted canon*
The Critical Darlings
A decade later, the episodic Gothic Noir that is Batman: TAS graced our TV screens. The serialized action-comedy-drama thriller that is Spectacular Spider-man aired in the following decade. These two are what transcend the medium that has the misfortune of being labeled a genre. Bruce Timm became a recognizable figure in the animation industry & cbtv. Paul Dini conceived Harley Quinn (did not co-produce; credited for far less ep than I assumed). As Batman TAS was WBA's crowning achievement in more dramatic fare, Greg Weisman was Disney's answer to Timm with the advent of Gargoyles. What sheer coincidence that a Spider-man series would be developed by him and another talented director, Victor Cook (Hellboy Animated, The Legend of Tarzan, Buzz Lightyear of Star Command). Content-wise, not since Batman TAS and Spec Spidey has the writing been this sharp, the directing this pristine, the acting this top-notch, the art this stylized yet remarkable, the animation this fluid, and the cities of Gotham and NY this fleshed out. The ensemble cast of supporting characters and villains are well conceived and from a wide enough variety of perspectives that they're believable as people, first and foremost. Their development also plays greatly into the titular leads' strengths, weaknesses, and relationships.
Team Centric
The above images and headline speak for themselves. Spider-man and his Amazing Friends is an extension of Spider-man '81 as much as The New Batman Adventures is an extension of Batman TAS. Spider-man got two new mutant companions and then, 2 decades later, Batman's family of caped crusaders fought alongside other heroes, whose origins premiered on this show.
The Futuristic Spin-off
In the final solo Batman series within the DCAU, Batman Beyond, Bruce Wayne has retired and, after some convincing, oversees the new dark knight, Terry McGinnis. In Spider-man Unlimited, Peter Parker, now married to Mary Jane Watson, ends up in a different dimension while trying to stop Venom and Carnage from hijacking Col. Jameson's shuttle. McGinnis' Beyond suit is high-tech and visually reminiscent of Miguel O'Hara's Spider-man suit. He fights crime in a Blade Runner-esque Gotham with flying cars and other advanced machinery. Parker's nanotech suit exhibits similar abilities as McGinnis' such as cloaking, different vision modes, built-in electric shock, and enhanced physical prowess (built-in web-shooters may = built-in retractable glider). Parker fights crime on Counter-Earth, where a technologically advanced NYC is overrun by anthropomorphic animals whilst humans are the oppressed species. Inversely, the marginalized members of futuristic Gotham are mutants, most of whom are criminals. Some of the previously established characters on BTAS and Spider-man TAS are re-imagined or updated to fit the scope of the reality amongst newly devised heroes & villains. Both shows also premiered/aired during the same 3 years. This might be the most contrived comparison since Batman Beyond aired 9 months before Spider-man Unlimted and the latter only had a season of 13 episodes.
Edgy Commercial
Both are, for the most part, on the serious spectrum of Batman/Spider-man shows ('you've been had'), but executed in such a way to be just another drop in the Saturday morning kid's show bucket. The most quality-driven aspect - the relationship drama Wayne, Parker & their villains engage in has been fairly sensible and emotionally moving at times. The fact is the crime-fighting is repetitive ep after ep with some variance and few standouts; merely meandering to get to a major event. They're also the longest running shows within their franchises.
*Rino Romano played Peter Parker/Spider-man in Spider-man Unlimited and then Bruce Wayne/Batman in The Batman*
Campy Contemporary
Intentional format and deliberately or squarely aimed at a younger viewership. Are there "heart string pulling" or some "unironic, well-crafted fun to be had" moments? Well, there are far more in one than the other, but the point is a comical or pun-fueled action show is what's to be expected. Other expectations? frequent team-ups, multiple cameos, crossovers, and showcasing an extensive list of obscure heroes and villains. Ultimate Spider-man has the added bonus of being a modern 80's toon and not so subtly presenting the lesson of the day in relation to characters who have to repeatedly be taught the same lesson...Batman: the Brave and the Bold has a better grasp on the action comedy duality as it embraces and successfully satires its Silver Age roots. Oh. and Ultimate Spider-man loosely adapts comics here and there. US-M was supervised by Man of Action (Ben 10, Generator Rex).
That one time they went full 3D
Beware the Batman succumbed to the other hip new trend, 3D CG animation. Back in 2003, Sony Pictures Television entrusted Rainmaker Entertainment (Reboot, Beast Wars, Beast Machines) to craft the first ever 3D CG Spider-man show that reflected the Raimi flicks. Thus, Harry Osbourne was a rich playboy... Beware the Batman continued Batman: the Brave and the Bold's focus on obscure heroes/villains to the point where more notable villains didn't appear until half-way through the season. Spider-man The New Animated Series had a limited run, thus was given a far less pool of characters to utilize (not nearly as obscure). Beware the Batman had a more Earth One feel to it, but was very reminiscent of Batman The Animated Series. Spider-man TNAS was vaguely reminiscent of 90's Spider-man and the Raimi films, but went for a more mature tone since it premiered/aired on MTV.
*Neil Patrick Harris voiced Peter Parker/Spider-man in Spider-man The New Animated Series*
If you made it this far, thanks for reading.