I've never read the Dracula comics, unfortunately, but I've read several novels and short stories, where other authors took the original Bram Stoker character and developed him even further.
As far as I can remember, merely some of his powers were -
Full and total control over the creatures of the night (wolves, rats, bats)
Mind-control (hypnotism, the ability to mesmerise, etc)
Metamorphosis (total and complete control over his own body, the ability to turn into fog, being completely intangible therefore, while still retaining full intelligence, as well as the ability to turn into any of the above-mentioned creatures)
Immortality (and need I mention the healing factor?)
Inhuman strength and speed
Experience (that comes from surviving, and not merely surviving, but thriving, for centuries.)
Above average intelligence, which combined with experience, gives him a powerful edge.
Some invulnerability
Then, of course, there is also the fact that as the most powerful vampire that has ever lived, he has gained some resistance to sunlight, crucifixes, holy water, and the rest of the holy paraphernalia.
Plus, he has all those creature-servants guarding him, as well as his lovers.
Looking at it objectively, I don't really think Batman could survive this.
Dracula is too fast, if he gets into trouble he can disappear before Batman can blink, and then take him any time he feels like it.
In a straight fight, with no holy weapons, Batman is a living dead man.
I think Batman might be able to hurt him, even stop him, temporarily, but ultimately, Dracula would triumph, as he has always triumphed.
And leave us not forget, Dracula is a merciless killer, a hunter-predator who has been preying on humans for centuries.
As Orestes said, the more pertinent question might be would Batman be able to escape with his life?