Symbolism, Imagery, Allegory
We can say this with certainty: Abraham Lincoln: Dragon Slayer would not be as good. And not just because it would be weird to be all like "no one knew that dragons really exist" when dragons are giant, flying, fire-breathing monsters.
Vampires are an excellent monster to use in this book for one giant reason: vampires are like people, but they think they're better than us. They're smug. In other words, vampires are a great choice for a book that also deals with slavery. After all, vampires feed on the blood of other people; and slave-owners live off of the blood, sweat, and tears of other people.
Abe makes this connection clearly after he watches vampires feed on slaves outside of New Orleans: "So long as this country is cursed with slavery, so too will it be cursed with vampires" (4.114).
Even vampires who don't eat slaves are marked as being very wealthy, not at all like the ordinary Abe Lincoln and his ordinary ax. When Abe watches the vampires eat the slaves, he notes that they all "looked to be men of some means" (4.108). And even the good vampires get associated with wealth.
When Abe meets the Union in New York City, he finds them in "a grand, two-tiered ballroom" with "Gold upon gold. Marble upon marble. The finest carvings and furnishings" (9.76). These vamps aren't like ordinary men in more ways then one. They would fit in much more on Madison Avenue than on Main Street. They're movers and shakers, and they aren't afraid to show it in their fancypants.
Kings and Tyrants
In fact, evil vampires are even associated with kings in this book. Now that's fancy. When Henry is describing the difference between good and bad vampires, he says that the good vampires remember what it's like to be ordinary people, while the evil vampires see themselves "As kings—superior to man in every way" (9.106).
And when Lincoln is debating Douglas and can't come right out and say "my opponent serves vampires" (like politicians say today), Lincoln drops a hint by saying that slavery separates out democratic, good rule from evil, tyrannical rule: "The one is the common right of humanity and the other the divine right of kings" (10.19). And even Jefferson Davis agrees with this connection between vampires and kings, noting that he's planning for a possible future where "vampires are to be the kings of men" (10.122).
Of course this whole tyranny thing might raise some eyebrows. Doesn't Booth shout something about tyrants when he shoots Lincoln? Something that amounts to "Tyrants are gonna get theirs in the end!"? If vamps are all kingly and stuff, what's Booth's beef with tyranny? Maybe tyrants are okay, as long as vamps agree with them. But if someone who is, say anti-slavery gets some power, well, then they're automatically a tyrant. Does that sound fair?
Lastly, here's one more reason why vampires work symbolically in this book: Abe Lincoln's story has a lot of death and loss. So, when you have one guy who really did lose his mom and his younger brother and his older sister and two of his kids, it's going to be a story with a lot of issues around mortality.
And that mortality is always vampire-related. Think about it. Vampires bring about death (of Abe's loved ones, specifically), but they also manage to escape it entirely. So vampires work as symbols both of death (they are already dead) and of life going on (since they stick around after they die).
And when Abe becomes a vampire, well, that must give him some major identity issues. He has spent most of his life hating these things that go on living at the expense of others, and now he is one. Yikes. Abe, there's this wonderful thing called therapy.
What's the point of all this? Well, it's proof that vampires are the perfect creatures for this novel. They work much better than zombies or werewolves would, because they're dead people who think they're better than living people, who live off the blood of other people. In other words, they're pretty much humans with a twist, and that makes for some interesting plot twists, too.