I will say that the 60s Spider-Man and Fantastic Four cartoons did come very close to capturing the spirit of the comics.
I don't know about the FF cartoon, but I definitely disagree about the '60s Spidey cartoon. It had the action of the comics, but left out the characterization, personal drama, and serialized plotting -- the very things Stan Lee added to comic-book storytelling that were so revolutionary and defined the Marvel approach. I don't think we got any Marvel cartoons that captured those aspects of Marvel's writing until the FOX X-Men
cartoons of the '90s. Those shows, especially the latter, captured the mix of qualities that characterized Lee's writing for better or worse: believable characterization and elaborate personal melodrama combined with wild, bizarre fantasy concepts and intensely corny dialogue.
I agree with this completely. I was fortunate I grew up in the 90s. On top of those two, we had the Batman Animated Series. I think part of the reason for the success of the new comic movies is that the children of the 90s are now into adulthood so they can appreciate these stories on the big screen.
Don't get me wrong. None are perfect. I was confused in the first Spiderman movie seeing Green Goblin before Hobgoblin, but I quickly figured out why there was a change. Likewise, there's an awkward habit in the first season of X-Men for everyone to refer to each other exclusively by their superhero name even when in private, but they thankfully fixed that in future seasons. Either way, the stories, themes, and characters of the comics were pretty faithfully captured for those fortunate enough to see them.