Comic books, like science fiction, often wanted to predict the future (i.e. the cover of Captain America #1 practically declaring war before the United States was even involved in World War I). The connection to science and modernism always kept the interest for most comic books. During the 1960s, the times were almost radical enough to be a science fiction. The fear from the Cold War in America shifted and gave way to a cultural change concerning civil rights and the emerging Vietnam War. Scientifically, America and Russia decided to compete for a different frontier: outer space. The emergence of TV made the family come together under one roof to watch news and current events, and also became an immense competition to the comic book industry. It was hard for writers to find an edge and attract its readers the same way television could, especially with the comic book codes in place.
DC comics had survived better than most publishers, codes intact. Even television could not hurt them completely, as they merely brought Superman to television. What DC did not do, however, was create a dynamic. Even the newly created "Justice League" that featured new characters did not create something fresh. Some, however, knew exactly the approach for a new era of comic books. Dell Publications, one of the most popular comic book publishers in the world, started regularly publishing comics (namely Jungle War Stories) devoted to the Vietnam War, one huge catalyst to the counterculture generation. Marvel writer Stan Lee found an advantage in staying on top of the times. With the creation of characters like the "Uncanny X-Men" and Spiderman, the Marvel name was put at the forefront of the comic book industry. Lee created The Fantastic Four not only to imitate DC's Justice League, but to elaborate on the "atomic age" in America. Many of these differences were implanted to bring a different style to the comic book industry.
The attitudes of the Marvel heroes starkly contrasted with DC's style. Superheroes also became less of a strange entity, unlike the "supermen" of the time. The Marvel approach took modern people, made some strange circumstance happen to them, and eventually they accepted their fate as super beings. Peter Parker was an average with a nerdy appearance and bad luck with girls…until an encounter with a radioactive spider. The X-Men were exclusively people with strange genetics that had mostly normal appearances. They almost did not have alter egos, because they were born seemingly normal. There was angst to them, even when they were supposed to be cooperative. They all had distinct personalities, but suffered modern ailments as well. The X-Men, as well as The Thing from The Fantastic Four, were regarded by society as "freaks", and that played into the realistic problem of segregation. In Amazing Spider-Man #68, Peter's campus (like many college campuses during the Vietnam War) was protesting. The problem was trivial compared to the Vietnam War, but it put the story on a platform that was easy to relate to. Feminist efforts were dashed in comic books, even in the most subtle way. DC's Justice League featured Hawkgirl and Supergirl (neither of which really changed), although their powers were stated as equal or similar to the powers of their counterparts. In Marvel comics, "Marvel Girl" was the codename for Jean Grey from the X-Men (until she was just called Jean), and Sue Storm was the "Invisible Girl" before she was the "Invisible Woman", one of the only real "women" in the 1960's. The dichotomy between (most) DC characters and the Marvel characters is that they were not instantaneously loved. Instead of being flashy and celebrated, Marvel superheroes were crafted like a well-kept secret.
So in many ways, comic books did not lag behind social times. Of course, there were some setbacks due to the comic code, but as long as nothing really offensive went through, nothing was censored. The opportunity to change the market and have a voice was present throughout the 1960's, and for the most part, the comic book industry took full advantage.