I'm halfway through the 1960's with the Hugo winning novels and the shift to a more "literary" science fiction is immediately clear. We're not quite to the New Wave yet but you can sense it building under the surface in novels like Stranger in a Strange Land and The Man in the High Castle. Even Canticle for Leibowitz shows some of the boundary breaking in my mind, though it broke in almost a completely opposite direction than where most of the rest of science fiction was heading.
Nuclear war is now a major reoccurring theme. You could see it starting at the end of the 1950's but in this block of novels Starship Troopers features nuclear armaments, it's at the heart of Canticle, and it is threateningly close in Castle and Way Station. In typing this it has occurred to me that some of Way Station's conflict may be intended to reflect the Cuban Missile Crisis which would have occurred about the time it was being written. As the cold war drags on the nuclear threat will fade into the background but it's still fresh and raw here.
One thing that strikes me is how earthbound these novels are as Starship Troopers is the only novel with a really traditional "outer space" setting. It strikes me as odd that in an era when space exploration was making regular headlines (positive ones, too!) that science fiction fans turned away from that. Was there a sense of "been there, done that"? Too much space in the real world making fiction go another direction?
The science fiction this time around seems more sociological than physical. Troopers had its merit based citizenship, Canticle examined the relationship between religion and society, Stranger was about an outsider looking back in on humanity, and Castle had an different version of history. The changes in the society were standing alone in these novels rather than being built on an external change. Compare that to A Case of Conscience where Blish uses aliens to drive his plot about religion or The Demolished Man which featured the changes caused by the development of telepathy. Canticle is the only one where you might make a case that technology has driven the change (in this case the nuclear bomb) but I think that the themes of Canticle stand apart from the post-nuclear war setting.
Currently the tally on my binary grading scale of liked/didn't like is:
Didn't Like: 2
I liked all five books in this block though I have some hefty complaints about the two Heinlein books (the lectures aren't that interesting in Troopers and the cult at the end of Stranger) and Castle is right on the border for me due to its very disjointed narrative. This will not happen again with the existing winners, though I'll spoil things and say that I think that all three winners so far in the second half of the 2000 block are pretty good.
One final note that may be of interest. There is one author who was nominated twice in this period and lost each time that most people may not expect. In 1960 Kurt Vonnegut's The Sirens of Titan lost to Starship Troopers and in 1964 his Cat's Cradle lost to Way Station. I'm sure he was crying all the way to the bank.