Between 1955-1985 we had the civil rights movement, the moon landing, the Vietnam War, and the final decades of the Cold War. Between 1985-2015 we've had the fall of the Soviet Union and the Berlin Wall, the Gulf Wars and Afghanistan, and 9/11. I'm obviously missing some other significant events.
We also had technological shifts - 1955-1985 saw records -> tapes, but CDs and PCs were not quite massively adopted yet. 1985-2015 has seen CDs -> flash storage, mass adoption of PCs -> laptops -> smartphones, and social media apps. Much of the advances in technology have connected us geographically and temporally.
I feel like the significant events between 1955-1985 separated the youth of the 80's from the youth of the 50's, more than the significant events from 1985-2015 have. I also feel that many changes between 1985-2015 actually connected today's youth to people and events of the last 30 years.