Science fiction is full of different societies. We also have a fondness for dystopias and utopias.
On the face of it a story set in a utopia would seem to be very different from one set in a dystopia. In a utopia, society is "perfect" - or at least substantially better than ours. A dystopia is a broken society. (Many writers also create societies that are neither, such as C.J. Cherryh's Cyteen, the libertarian society of Starship Troopers, etc).
But the thing which hit me.
A story about every day life in a utopia is boring. There's really two good ways to go with utopian stories. The first is the Star Trek method - set your stories out on the frontier where society is still rough around the edges and make it about the people who agree life in a utopia is boring. The second is to write the story about the person for whom the utopia, well, isn't. The person who doesn't fit in.
The dystopian story is, by definition, about the person who can't fit in with their twisted society. The difference is that when the person doesn't fit in in a utopia, the fault is in the person (James T. Kirk doesn't fit in on a nice, quiet, tamed Earth - but fortunately they have a frontier to send him to) more than the society. By definition in a dystopia...
Which brings me to the thing they have in common.
A utopian story and a dystopian story both cast society to some degree as the antagonist.