1. Prequels fill in the gaps, while reboots mess with the plot.
We never learned that much about Carrie's backstory on Sex and the City — and that was OK. But the appeal of The Carrie Diaries is that it takes a story we already know and fills in the details we never got. Instead of scrubbing clean the Sex and the City we know and love (that is, the series and not the films that came after), the new show just enhances it by letting us know what happened before.
A fresh take is nice, but there's no need to mess with the original. Prequels leave the timelines intact (a few inconsistencies aside), and we don't have to deal with some whole new version of a favorite. The shows become completely separate entities that work as different parts of the same story, instead of overlapping one another. We don't need a fully reinvented Carrie Bradshaw. Speaking of...
2. Prequels explore existing characters instead of creating new ones.
Just as we don't need a brand new Carrie Bradshaw, we don't need a new Hannibal or, in the case of Bates Motel, a new Norman Bates. We're getting different actors in the roles, but the characters themselves are the same — they function as part of the same continuity. (This is a little iffy in the case of Norman, as Bates Motel is modern-day and thus less clear-cut.)
With reboots, it's simply a matter of recasting beloved roles; in prequels, we're getting a younger version. The aim is to find someone who could conceivably grow up and become the established character, and that's far more interesting than offering a new take on the character that fully breaks away from the original. There's a reason we liked him or her in the first place.
3. Reboots try to modernize, but it's always more fun to go back.
One major point in The Carrie Diaries' favor is that it takes place in the '80s. We love the '80s — the fashion alone makes The Carrie Diaries worth watching. This is what distinguishes the prequel from the remake, which endeavors to bring an older franchise into the 2010s. What made anyone think we needed modern-day versions of Melrose Place or Charlie's Angels? As their failure indicates, we didn't.
Sure, nostalgia is fun, but it's about more than that. There's this frustrating notion that established shows need to be dusted off and tweaked with in order to be palatable to a modern audience. (Again, we'll leave Bates Motel out of this discussion, though I'll note it's still a much better idea than Gus Van Sant's Psycho.) Why pull series into the future when they worked so well in the past?
4. Prequels appeal to existing fans, while reboots focus entirely on new fans.
Look, when you're returning to an established franchise, it's always about milking it for more money. But reboots are the worst examples of this, because they tend to not give a crap about the hardcore fans. Case in point: the planned Buffy the Vampire Slayer reboot, which Buffy obsessives rejected like Ipecac. Prequels and sequels respect the original, making them a lot less traumatic to those of us who don't deal well with change.
And ideally, the new series will bring in new fans, anyway. It's just that there's a way to do this that doesn't crap all over the lifelong devotees. People who have never seen Psycho — shame on them, seriously — will tune in to Bates Motel. It might even inspire them to Netflix the Hitchcock classic. But those who know and love it can still appreciate a show that portrays a different time in Norman's life.
5. Prequels have a built-in end point, which builds tension.
This applies more to shows like Bates Motel and Hannibal. (What dark future can The Carrie Diaries portend, other than Sex and the City 2?) But for characters like Norman Bates and Hannibal Lecter, it's thrilling to know what they'll turn into — and see how they got there. That's why we were so excited to see the transformation of Anakin Skywalker, until the Star Wars prequels turned out to be shit.
The root of evil is a fascinating story. In that regard, prequels can be exciting even though we already know the ending — it's the pleasure of watching a tale we're familiar with unfold. This goes back to prequels filling in the gaps. We'll tune in to Bates Motel and Hannibal precisely because we know where they're going. What we don't know is how.