These decades stand out as especially changeful for music.  Most decades, such as the '80s, '00s, and '10s experience a slow evolution in music.  While music does change and is usually different at the end of the decade than it was at the beginning, most decades don't experience the magnitude of change that the 1960s and the 1990s did.  The '90s beganHere are some videos to show what I am talking about.

1960s:

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1990s:

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I would say the 1960s because the structural and thematic possibilities of music evolved so much more that decade. Everything in 1960 was so rote, unimaginative, corny, and repetitive, relying on mostly lame lyrics and the exact same basic chord progressions over and over again. That's a pretty far cry from the same year that brought us the Beatles' Abbey Road, Led Zeppelin's first two albums, In the Court of the Crimson King, the Velvet Underground's self-titled album (not the Andy Warhol banana album with Nico, though that was also a million years beyond early 60s music), and a pop landscape full of rich Motown soul that was just started to integrate early 70s funk influences as well.

The 1990s may have felt transformative, and in some ways they certainly were, but the thing is, the fundamental elements of pop songs from 1999 can still be reasonably compared to ones from 1990. There was already lots of alternative music popular in 1990, even if hair metal was still the mainstream standard. Y2K era teen pop is really just new jack swing and certain late 80s styles with newer instruments. Compare the beat for "Baby One More Time" to George Michael's "Monkey" or Bobby Brown's "Don't Be Cruel;" it's pretty much the exact same idea, but with much more polished instruments. The Backstreet Boys and *NSYNC were just New Kids on the Block all over again, just with more updated instruments but more or less the same attitude as before. I could easily imagine either group performing "You've Got It (The Right Stuff)" if it had been produced with Max Martin instruments. Much of the pop rock from 1999 was really not super different from what was already possible at the start of the decade; many songs still sounded like late 80s/early 90s R.E.M., and Sixpence None the Richer's 1999 cover of "There She Goes," originally made in 1988 and popular in 1990, sounds exactly the same, just in a different key to suit the different vocalist. Hip hop had come some ways since 1990, especially with Timbaland and Dr. Dre's influence over production, but even still, 1999 songs by Naughty By Nature and Will Smith can still be tied back to the early 90s (both were already popular back then), while lots of hip hop from the beginning of the decade, like Ice Cube's first few albums for example, had the same defiantly profane lyrics and dangerous attitude that was common practice in rap music by the end of the decade.

Late 90's music ended up being much softer and more 'feel good' than the early 90's.
Late 60's music ended up being overall more creative than the early 60's

I think I'm gonna go with the 60's on this one. I am partial to this decade but I honestly think there was more change. Music well and truly progressed throughout the 60's decade. The songs of 1969 really do feel a world away from the songs  of 1960 to me. I think the culture helped make late 60's music what it was in that there was a lot of change and unrest going on but there was also idealism and optimism for the future (Dawning of the age of Aquarius!) and psychedelia which lent themselves towards a more creative environment I think.

The 60s. 1965 is called "the most revolutionary year in music" for a reason.

By far the 60s. By far. Magnificent, creative, innovative, constantly changing music was pouring forth on a nonstop basis. And it was easy to embrace it all, no matter the style. Joan Baez shared bills with Jimi Hendrix. Donovan was backed by Led Zeppelin. Jimi Hendrix covered Bob Dylan. led Zeppelin adored Joni Mitchell. There weren't these little fiefdoms like, "oh, I like emo I don't like trap or zip or zap or this or that music".  All that divisiveness came later. No decade compares.

Definitely the 1960s. Even the adult contemporary shifted from a sound with heavy, choir-like orchestration to something more resembling the ballads of what the first wave of rock artists had done a decade prior. Obviously rock went from "Stuck On You" and "Running Bear" to "Whole Lotta Love" and "Come Together".

I'd even say the '70s were more changeful than the '90s, going from Three Dog Night and the twilight of Motown's golden age in 1970 to the electro-disco, post-punk, new wave of 1979 that even had the beginnings of the music video with songs like "Pop Musik", not to mention the dawn of hip hop.

I think the '70s and '80s were both just as changeful as the '90s.

Glam, prog, disco, funk, punk, and synthesized music really took of in the '70s.

Hip hop, house, freestyle, thrash, glam metal and alternative rock took off in the '80s.

Grunge, trance, ambient, nu metal, and gangsta rap really took off in the '90s.

If you compare the two end points of any of these you'll see some pretty radical changes.

But clearly the '60s are in a little category of their own. 1960 and 1969 feel like they're two or three decades apart.

1960

http://www.youtube.com/watch?v=xbK0C9AYMd8

1969

http://www.youtube.com/watch?v=4AKbUm8GrbM

Nuff said.