I think TAS, more so than perhaps any other cartoon, understood exactly what defines the styles and conventions of film, comic book, and animated cartoon, and understood how to combine and balance their strengths and limitations.
It aspired to tell stories of recognizably human characters with understandable, even empathic qualities, that weren't (and still aren't, really) considered feasible with cartoons or comics.
It took full advantage of the stylized visuals, dynamic characters and straightforward plots of comic books.
And through animation it was able to bring these characters to life with the physical stunts, deranged theatrics and sublime action that Batman needed.
The show's fundamental understanding of the differences between these art forms, and desire to blend them together to create the ultimate take on Batman, was so crucial to it's quality that the worst episodes are generally viewed as those that lose this balance and either devolve into silly and unremarkable cartoon or comic plots or wordy and melodramatic attempts to imitate film's moral gravity and drama.
I think it's a testament to the show's quality that these episodes don't constitute the majority and that even the show's failures can serve as lessons in storytelling.