Dracula, according to many critics, was always supposed to be sexual. The book has that one scene where the female vampires try to suck blood from Jonathan Harker and he gets real uncomfortable for more than one reason. It seem there is debate over exactly what the book has to say about sexuality (many consider it a warning tale), but it seems to be there. I imagine it's because the neck, though not as much today, has historically been shown off in a sort of sexual way, like the legs. Also, it is a place of intimacy and the "bite," a kind of penetration, lends to a feeling of sexual violation. Given that the book was written when Freud was active and popular, it's certainly plausible that this was the line of thinking. To me, there are similarities between Dracula and Don Giovanni from the Mozart opera of the same name who basically goes around using his influence to either seduce or rape women.
But, yeah, then there was Murnau's Nosferatu and Browning's Dracula and, like that, Dracula was a part of pop culture, with parodies such as Abbott and Costello Meet Frankenstein (in which they also meet Dracula) and The Count from Sesame Street, b-movies such as Billy the Kid vs. Dracula, all of which both/either blurred Dracula's previous meaning and/or softened his image a bit. Basically, what the vampire was previously was now fair game. To some degree, the sexual vampire persisted, but there were more representations of the vampire present.
Given that us amateur writers like to write stories where the dragon is good (because dragons are cool af) and the main character is a half-blood whatever (because they need to be edgy but not too edgy) and rely on a pop culture knowledge of things, it is very possible that stuff like Twilight was written only having met Dracula in a Scooby Doo special. Or, rather, how the vampire was going to be portrayed was likely decided in Stephanie Meyer's mind before she did any research. Used because the vampire is cool and not because the vampire represents anything (not that there is anything wrong with that; as I said, the vampire is fair game).
Also, given the whole Hot Topic phenomenon, it was only a matter of time before vampire media started catering more specifically to that crowd— younger, hornier, the logical audience for high school settings and steamy romance scenes.
Personally, I'm partial to the darker depictions. Dracula is pretty heckin' scary, mainly in that he almost always gets what he wants. The Harkers, Van Helsing, and the gang fail against him several times before they finally get him. And the whole thing with the ship and the guy in the mental institution as Dracula is traveling to England. And Nosferatu which takes out the sexual elements in favor of an almost apocalyptic vision of the vampire. And Dreyer's Vampyr which focuses on the occult aspects. And Silus from The Graveyard Book who's a stoic protector of the MC.