Mid-late 60s: Closer to the 1930s or 1990s?

There are plenty of points of comparison to be made here. In terms of technology, though it was a lot less sophisticated than 90s digital technology, I also think there are some aspects more similar to the 90s than 30s. For one thing, TV was a major form of entertainment in the 1960s as a whole, which they weren't in the 30s. Whilst movies do have some similarities to 30s movies, the mid-late 60s proved to be a MAJOR turning point in the film industry. This was due to the revocation of the Hays Code, which allowed for more mature and darker themes to be explored in movies, action movies filled with tons of death, cruder and darker humor in comedies, and horror to really take off as a film genre once again, but much bloodier. In addition, important movies like Bonnie and Clyde, The Graduate, 2001: A Space Odyssey and Planet of the Apes helped usher in a new era of filmmaking called New Hollywood, which was very distinct from the more wholesome if cliched movies of the Golden Age. These movies were based more on the directors instead of the actors. America's dominance over technology was also receding in the 1960s, as Japanese companies like Sony were quickly innovating whilst American companies like RCA struggled to keep up. Vacuum tubes became obsolete in this era, replaced by transistors in everything from radios to televisions, and it was this innovation that led to the consumer electronics boom of the late 20th century. Rotary phones weren't obsolete yet but push-button telephones also became a thing in the mid-late 1960s that would be the norm in the 90s. Rock music was a popular genre of music in both the 60s and 90s. Cartoons were now most popular on TV instead of theatrical shorts, which certainly ties them closer to the 90s instead of the 30s.
This era also saw the Civil Rights Act, which made segregation illegal. Blacks and minorities in general were starting to make their voices heard, and though acceptance wasn't anywhere near as good as it would be in the 90s, it wasn't as horrendous as it was in the 30s. Because of the counter-culture, as you said, fashion was closer to the 90s than the 30s. Top hats weren't fashionable anymore, or anything formal. The 60s in general had a casual vibe that the 30s didn't.
That said, there are still some differences as well between the mid-late 60s and 90s. For one thing, the Soviet Union was a thing during this era, and I think that's what Telso was trying to get at here with the Cold War era being more similar to the interwar period compared to the post-Cold War period. We weren't at war with the Soviets in the 30s, but their mere presence does tie this era in with the 30s in contrast to the 90s. And as Telso mentioned, CGI wasn't a thing. Computers were only used by scientists and in universities, and video games weren't a thing. And whilst we did have rock in the 60s, there was no rap, and pop in general was made with live instruments instead of electronics.

There were tons of rock music in the mid-late 60s, so it would be a tie because of that.

I see but 60s rock is closer to the 90s by default.