If someone mentions the Sixties, you immediately get some very clear, very striking, very consistent, and very strong images and impressions about cultural elements. Hippies, the peace movement, the Age of Aquarius, experimental drug use, the Summer of Love, and the invention of what is now called "classic rock" are all very firmly associated with the Sixties, so strongly that you could easily allude to any of them just by referring to the decade. (As I wrote once before, the calendar decade and the cultural decade are offset by 2-3 years, but that's beside the point.)
You can probably find similar associations for the other decades on either side. The Fifties bring up ideas of poodle skirts and greasers, unrestrained optimism in the promise of technology and industry, chrome fins on everything, and doo-wop music. The Seventies suggest fads like pet rocks and mood rings, disco, advancing into stronger drugs, and an all-pervasive superficiality and shallowness. Keep going through other decades and filling in your own answers.
But the farther you get from the Sixties, the weaker the associations get, particularly as you advance to more recent times. We can talk about the Eighties as the decade of MTV and Reaganomics and unrestrained capitalism and greed, but it doesn't seem to gel as well as the Seventies did, let alone the Sixties. And trying to talk about the Nineties is even blurrier. We could say that the Nineties are the decade of the Internet, of more global and environmental awareness, and a few other things. But the answer always ends up far more vague and less compelling than the Sixties, or it ends up being very personal -- what the Nineties mean to you, not what they mean in themselves the way the Sixties have a clear meaning.
How much of that is because it's more recent, so we don't have as much distance from it, as much time for the imagery to coalesce and distill down to essentials, or because we experienced it so it's harder to reduce it to a few archetypal images? Certainly some of it, but I think that even if you subtract that out, there's more to it. After all, the Thirties or Forties are almost as blurry as the Eighties or Nineties, and that's not all because they're far enough away to become history instead of culture.
Maybe that's all it is: someone born ten years after me will always find the Seventies the most clearly-defined decade because it's all about the "sweet spot" relative to one's own birth. But I doubt it. My suspicion is people born in 1997 will never think of the Nineties as having as strong a character as the Sixties do now, and have for most of my life. I think even after you subtract out these various factors, it remains that the Sixties just had more of its own character that can be described concisely but powerfully. And more recent times are more blurry because it's a larger smear of many smaller events due to the world's increasing informational interconnectedness, so there may never be another Sixties or Seventies again, at least not in the immediate future.