At the same time, though, these trappings and constructs can sap the visceral power of vampire-as-monster. They're hard work to get right, they're convoluted, and they're often dry. Memorization is thinking, and thinking runs counter to feeling, and if you're thinking too hard about the latest Coterie chart of which vampire is related to who, you're not crapping your pants with terror because some ancient beastie is going to sink its fangs into your neck.
And that's where zombies get another advantage in the fight for screen time. They're easy to understand, they're accessible, and they're not over-intellectualized. You can get right to the good stuff with a zombie (good stuff being defined as "blood and guts") without having to learn how they interact, who was a zombie first, and so forth.
Indeed, the fact that zombies are barely individuated (if at all) could be the key to the whole thing.
Whose Apocalypse Is It Anyway?
As far as supernatural end-of-the-world scenarios go, the zombie apocalypse would seem to be one of the less threatening ones. Sure, if you get chomped you get zombified yourself, but zombies are slow, stupid, and not terribly good at defending themselves. There's a reason The Walking Dead isn't called The Running Dead, The Sprinting Dead, or The Crawling Through The Air Ducts Ready To Drop Down On You Like Goddamn Batman Dead; it's because its zombies ... just ... walk. Any logical resistance involving things like roadblocks, flamethrowers, bulldozers or locked stairwells would seem to put a pretty significant crimp in the inexorable zombie advance.
A vampire apocalypse, on the other hand, is a much scarier proposition. Vampires are smart. They're fast. They have - depending on which version of the myth you play with - magical powers. Their bite turns you just as surely as a zombie bite does, and it takes more than a slug to the head to take one down. And that's before you start adding in the various Renfield types under their control. Put a closed door in front of a zombie and he'll keep walking into it. Put it in front of a vampire and he'll turn to mist and waft in through the keyhole, or climb the outside of the building, or, well, let's just say your odds of being completely screwed are a lot higher.
But it's the zombie apocalypse that everyone talks about, jokes about, buys books about, and tweets internet memes about. That's our monster-driven eschatology of choice (sorry, Cloverfield). Vampires, instead of wanting to take over the world, seem to have bought whole-heartedly into the LARPy notion of hiding in plain sight, dwelling among humans and hoping not to attract too much attention while they do it. Even balls-to-the-walls vampires in films like Let the Right One In blend with mortals - they move from place to place, they operate through human catspaws, and they run rather than make a stand. They're not interested in ruling the world, just in continuing to survive in it.
And that, perhaps, is the last piece in understanding why vampires have moved to the sidelines.