1. Moral ambiguity.
Let's get this out of the way first: Klaus is not Angel. As tempting as it is to compare the two vampires, Angel on Buffy was — for the most part — a sensitive, kindhearted soul. When he was Angelus, he did his share of damage, but his default state was as a force of good. Klaus, on the other hand, is always kind of evil. While he has his own set of morals, they often involve killing innocent people. (Case in point: drowning Tyler's mom just to avenge Tyler's slight against him.) At the same time, The Originals is exploring a different side of Klaus. If he can't be good, can he at least be someone we root for? Angel, too, had to deal with the darker elements of his personality throughout the course of his spin-off. It's not about being a hero or a villain but rather finding a balance. Audiences love a complicated protagonist.
2. Darker tone.
The contrast between Buffy and Angel was clear from the get-go: Sunnydale was bright and open, Los Angeles was dark and seedy. In the same way, The Originals has established New Orleans as a more dangerous, adult location for its characters. It's not that Mystic Falls was ever safe, even without a Hellmouth. But visually, New Orleans is filled with shadows and a constant feeling of uncertainty. And Klaus, who could easily be in charge on The Vampire Diaries, is no longer the head of the pack. The key to The Originals, like Angel, is to heighten the stakes by repositioning the characters in a city in which they — and the audience — feel uncomfortable. The result is a show that suddenly feels more mature, which is a great way to break away from its teen drama predecessor.
3. Secondary character steps forward as strong female lead.
The Originals and Angel are both spin-offs centered around a male character, but thankfully they compensate with several strong female characters. The Originals, in particular, has done an impressive job creating a diverse cast. But the character of Hayley specifically seems modeled after the Cordelia Chase school of character development, in that she showed up on The Vampire Diaries without much to do and then transitioned to The Originals as a more independent, assertive lead character. To be fair, Hayley was always stronger than Cordelia: one is a spoiled rich girl, and the other is a werewolf. But they are both women who were initially pushed to the background but who, on their respective spin-offs, can hold their own against the male leads.
The Vampire Diaries and Buffy the Vampire Slayer both used flashbacks to their advantage, so it's not like their spin-offs reinvent the wheel. Still, The Originals is doing a good job of employing flashbacks to fill in the blanks in their characters' histories. (How did Klaus and Marcel meet? What was his relationship with Rebekah? Where did the friendship take a turn?) Angel did the same thing: We knew Angel's backstory from Buffy, but there was still so much to flesh out, as we later learned from repeated trips through his memories. Shows like Once Upon a Time and even Lost have relied too heavily on flashbacks. They can't be the primary storytelling device. But as an occasional method for showing rather than telling important character dynamics, flashbacks can be very effective.
5. Focus on supernatural over humans.
Who cares about normal humans when you've got vampires, werewolves, and witches to deal with? The Originals doesn't waste too much time with the human population of New Orleans, and that's a good thing. Angel, too, gave us a much more fantastical, demon-inhabited world than anything Buffy had offered. These spin-offs come years after the originals, at which point we already accept the existence of vampires and other things that go bump in the night. By putting more emphasis on the supernatural, the shows become about high-stakes supernatural conflicts rather than chronicling the drama of trying to survive as a human in a supernatural world. The latter is an interesting story, but it's one we've heard already. And we know how that turned out for Elena.
6. Angst over the girl left behind.
Wild horses couldn't drag Angel away from Buffy — but they kind of did. (Or, OK, some stern words from Buffy's mom helped.) The point is, Angel began with heartbreak, and that's something that carried through the first season. Klaus and Caroline never consummated their relationship the way Buffy and Angel did, but their seemingly inevitable romantic pairing was something fans clinged to nonetheless. As such, there's a sense of loss to The Originals, something that was underscored when Tyler showed up and reminded Klaus of the woman back in Mystic Falls. To some extent, Rebekah's brief but meaningful fling with Matt carries the same potential, though Rebekah seems to have moved on pretty quickly. And who can blame her? Marcel is dreamy.
7. First crossover is a threat.
It's tempting with a spin-off to immediately do a crossover where the original characters meet the new characters and sparks fly. The Vampire Diaries is very much doing its own thing, though, much as Buffy did in Season 4 — and that allows the new shows to grow on their own as well. The only crossover we've seen so far on The Originals is Tyler, who traveled to New Orleans to get his revenge on Klaus. Similarly, early in Angel's first season, Spike showed up to terrorize his frequent adversary. These crossovers destabilize the norm: On The Originals, we're suddenly supposed to think of Tyler as a villain. But they're great reminders that we're dealing with two very different series that happen to take place in the same universe. It's about the story, not pandering to fans for ratings.
8. Mystical pregnancy.
Can we get a little specific here? Both The Originals and Angel explore the "But I thought vampires can't procreate!" dilemma. In Angel's case, it took till Season 3 for Darla to return to Los Angeles with a hefty baby bump. The Originals, by contrast, introduced Hayley's pregnancy as one of the central Season 1 plot lines: What happens when an original puts a baby in a werewolf? Either way, the result is the same — like the darker tone and characterizations, pregnancy ushers these characters further into adulthood. The baby-to-be is not treated as a teenage mistake either. Instead, it's all a part of growing up, which for Klaus and Angel means accepting a new role as a father. Scary, isn't it? Let's just hope Hayley has an easier time giving birth than Darla did.