Not really. The 2003 animated series was extremely faithful to the comics, adapting many of their story arcs directly and taking a more serious tone than the previous cartoon (at least until the last couple of seasons where it was more kiddified). The current animated series blends elements from both previous shows and the comics, and has its own distinctive tone and style. The first live-action movie was also relatively serious and was the first adaptation to draw on the "retreat to April's family farmhouse" arc from the comics, which has been a staple of most subsequent adaptations (even taking up nearly the entire third season of the current show). That's one of a number of elements that have recurred in multiple adaptations but were never seen in the '87 cartoon, including Shredder's daughter Karai (first seen onscreen in the '03 series, also featured in the animated movie and the current series), the Purple Dragons gang (featured in the second and third animated series and slated to appear in the next feature film), and the outer space arc with the Triceratons and the Fugitoid (featured in both the second and third animated series -- although the Triceratons did briefly appear in a single episode of the '87 series).
This was not the case in the original live-action movies or the 2003 series. Both of those went with the comics' version where he was Hamato Yoshi's pet rat. (Which never made sense to me, really, since it required the rat to be fairly anthropomorphized even before his mutation.)
This was not the case in either the 2003 animated series (where she was a scientist who then became an antiques dealer) or the current one (where she's a schoolgirl training under Splinter as a kunoichi). She was an adventurer in the '07 animated film, although that was a loose sequel to the original film trilogy, so presumably she was a former reporter there.
Again, none of these were featured in the original movie trilogy, its 2007 sequel, or the 2003 series. The '03 series used the Utrom, the aliens from the comics that Krang was very, very loosely based on. The current show's Kraang are basically evil Utrom -- something that was made explicit in a recent story arc, revealing that the species is actually called the Utrom and the Kraang are a militant faction that took over their civilization.
These are the only elements introduced by the '80s cartoon that actually have been kept in every adaptation. The bandana colors were kept because they're simply a good idea; the Turtles were too hard to tell apart in the original comics. (Note, though, that none of the other adaptations have kept the '87 Turtles' initialled belt buckles.) As for pizza... well, who doesn't like pizza? (I don't think it was played up quite as much in the '03 series, though.)
Those are some very fair points and I agree that the multicolored bandanas were a very good idea and also prefer Splinter as Hamato Yoshi turned into a mutant rat (esp. since it makes the Splinter/Shredder feud far more personal).
I'll admit I was generalizing, however, I still think the '80s cartoon overshadows the Mirage comics as far as influence goes on the franchise. (The only direct adaptations I'm aware of these versions of are in the
Turtles Forever movie finale to the 2003 cartoon continuity and it's pesudo-remake as the "Trans-Dimensional Turtles" episode in the 2012 cartoon continuity).
For example, you commented that the 2012 cartoon is largely it's own thing. While that's true, since there's a lot of new characters, exclusive parodies of other properties, and old characters and elements tend to get revised origins, the vast majority of old elements are from the '80s cartoon. The mutagen works the same way as it did in the '80s and we get stuff and characters like the Party Wagon, the Turtle Blimp, Dimension X, Foot bots, Mutagen Man, fly mutant Baxter Stockman, Pizza Face, Bebop and Rocksteady, Slash, Muck Man, Mona Lisa, the Neutrinos, Lord Dregg, etc.
There are elements from other iterations of the franchise, like the Earth Protection Force, Bishop, and Hun from the 2003 cartoon, Armaggon and Belly Bomb from the Archie comics, adaptations of the "City at War" materials and other ideas (like Leatherhead being a good guy) from the Mirage comics (plus the inclusion of any Mirage original characters), and several easter eggs to the original movie in the North Hampton episodes (April reading her journal in voiceover, Splinter being seen in the campfire, etc.). But, the '80s cartoon is still the defining source of inspiration. It's a similar situation for the new movie series, esp.
Out of the Shadows. To the best of my knowledge, aside from three or so elements cribbed from 2012 series (Baxter Stockman, Rocksteady's real name, and Casey Jones rollerblades), that movie takes every pre-existing thing from the '80s show.
On a final note, regardless of the incarnation, every version has based the Turtles themselves squarely on the '80s version (Raph notwithstanding). If that's not dominate influence, I don't know what is.
(To continue the TMNT parallel, I'd also argue that that Abramsverse movies wanted to be their franchise's version of the 2012 show; a remake that took its own spin on the source material, but was still recognizable as the source material -- and, by chance, even grandfathered older material as a parallel universe in the same multiverse, albeit TMNT 2012 did establish that 2003 TMNT cartoon was not in continuity.
However, the difference is is that TMNT 2012 understood how its franchise works, so they are able to reimagine elements in a way that still feels organic, whereas the Abramsverse has a lot of in-jokes and recycles stuff, but really doesn't understand what it's playing with, so things don't feel quite right. I find it also telling that that the TMNT 2012 production team is staffed by fans of the '80s cartoon, while the Abramsverse takes pride in the fact that the people steering the ship are not
Star Trek fans. While having fans working on it doesn't mean the product will be great -- Spider-Man comics have been suffering because of fans working on the property -- I think it's very interesting that TMNT 2012 has become considered one of the best installments in its franchise, while the Abramsverse has a mixed reception with its. Your mileage will vary with all this, of course.)
As I've said before, it makes no sense to expect a television series in this universe to have the same action-heavy emphasis as the movies, because they simply couldn't afford to. TV shows are a different medium from movies with their own distinct strengths and weaknesses. The previous Trek movies tended to be more action-driven and spectacle-driven than the TV series they shared a reality with. And look at the Marvel Cinematic Universe -- compare something like Age of Ultron to something like Jessica Jones. They're totally different in tone, style, and emphasis. Big-budget movies tend more toward action and spectacle, TV series tend more toward plot and characterization. Those are their respective strengths, in any continuity.
I'd love to see some of the MCU TV shows beyond
Agents of SHIELD (DVD/Blu-Rays, please?). However, I'd point out that the
Trek movies also tended to be far more character-driven than other blockbuster movie. For example,
First Contact's action is driven by Picard's obsession with revenge on the Borg. There's battles and fights, but the drama is focused on on man dealing with his demons, not stringing together action set pieces for exciting battles. The "B" plot has the the characters meeting a historical figure and learning that the lionized version that the history books have presented was very wrong. That's both stuff I feel that the new movies have botched, as the character's take a back seat to the plots, which are written to best string up cool actions scenes, rather then writing the action scenes to best fit the narrative. So, my feeling is that the old movies in general knew how to balance the stuff that made
Star Trek Star Trek, but still have it on a bigger scale, while the new movies are trying to twist the franchise to fit a formula that it was never meant to be (and doing it at the expense of the writing and characters, to boot, which are the real benchmarks for a stories success).
Heck, part of the value of a multi-series franchise is that it lets you incorporate multiple different storytelling styles and tones. There'd be no point in expanding a continuity across different series or different media if they were all exactly the same. Look at the stylistic differences even between things in the same medium, e.g. Deep Space Nine vs. Voyager, Torchwood vs. The Sarah Jane Adventures, Arrow vs. Legends of Tomorrow, etc.
Fair enough, and while I don't like the new
Trek movie series (I will admit that the second trailer for
Star Trek Beyond makes the movie look promising, but I've already been bit twice, so I'm not very trusting right now), I don't think they don't have a place. If that's what some people like, fair enough. (I am willing to debate its merits and wether it works in the context of being a
Star Trek film series, but that doesn't mean that others shouldn't be free to love it.)
I'd just like to see a future
Trek movie or TV show return to its roots and tell something that feels like the prime universe version of
Star Trek (whether they do that by continuing the prime universe, writing a movie in the Abramsverse that functions like a throwback, create a brand-new continuity, etc.). That's what I like about this franchise and the reason I watch it.