Dystopian literature is, technically, a form of science fiction. Since we are dealing with stories based on reality, we have to have a reason WHY the world turned bad--and in order to do that, we have to use science. We can't use magic, we can't cheat our readers and say "just because"--we have to ground our works in reality so that the readers can reasonably say, "Hey, yeah...that COULD happen..."
But how much science do you need? In today's dystopian literature, I think it's easy to put the HOW of the science on the backburner and focus instead on the WHY. In Mary Pearson's THE ADORATION OF JENNA FOX (slight spoilers ahead), we're told that the main character's medical problems are solved with a mysterious genetic substance--something we clearly don't have currently, but is something we are able to suspend our disbelief in and accept. A fan of hard science fiction would probably argue with this presentation--hard sci fi readers want to know HOW the science works. But teens and readers of teen lit tend to care much more about the WHY. It's enough for us that her parents use the mysterious substance and that the substance isn't so outrageously beyond our scope of knowledge that we question it. What's much more important is WHY her parents are willing to use the substance. That's the meat of Pearson's story.
Joss Whedon's FIREFLY and SERENITY.* There's all sorts of technology out of our reach on this world--paper that's an electronic screen, space crafts that travels faster than the speed of light, hover vehicles, goo that seals wounds, etc., etc. But all these modern marvels are relegated to background and props because what we really care about is Captain Mal's ethical dilemmas, River Song's mental illness, Wash and Zoe's marital problems, and whether Shephard Book's story will ever fully be told (yes--in graphic novel form), whether Kayleigh and Simon will hook up (yes--and how creepy is it that River watches?!), and whether or not Jayne is actually a big damn hero (duh, obviously so!).
Characterization over science isn't limited to teen literature, though--just as dystopian literature isn't limited to teens. Think about Cormac McCarthy's THE ROAD. This is definitely an adult dystopian...but it, too, focuses primarily on characters over science. We don't really know exactly why and how the world ended up so bleak and terrible--all we really know is that it IS bleak and terrible, and a father and son must find a way to live--or not--in such a world.
In the end, I think this leads to one of the key differences between science fiction and dystopian literature. Both deal with a different world from the one we have now, and both explain the world's differences through science. But science fiction tends to focus on the how--the science of the situation--while dystopian tends to focus more on the why--the characters in the situation.
*One could argue whether SERENITY and FIREFLY are more accurately labeled sci fi or dystopian...but I posit it's a far-future dystopian. Take away the space ship, and you've got all the classic tropes of dystopian--cruel government, gang of rebels fighting the government, a world that's lost a lot of it's former hope and innocence.