If we are going by stereotypical Vampires then the reasons why Vampires would win are as follows:
1. They are Immortal
By being immortal the Basilisk can not kill them Via staring or biting.
2. Vampires can turn into bats which are fast and use echo-location
If the vampire turns into a bat then the Vampire will have the ranged advantage and can simply swoop in whenever it needs to.
This applies to the Mythological Basilisk (Not the Harry Potter one)
3.The Basilisk is short and probably couldn't do anything to the Vampire and they can then probably squish it.
This applies to the Harry Potter Basilisk
4. By blinding the Basilisk it will then be completely blind and can have trouble finding the Vampire (Bat form) and will therefore not be able to see its next attack especially if in a loud area.
Basilisks are way bigger. Even though vampires are fast and are immortal, it doesn't make them immune to injury. Vampires can get injured and get drained of blood which make them die because they survive on blood. So if a basilisk bites them and drains there blood, they will die.
In the book series cirque du freak it says vampires are allergic. I run out of things to say so the rest of this is nothing.
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A sparkling, glittery vampire with 5 cars, ocher or black eyes, and a wish to stay in high school for 100 years? Um, heck no. But an actual vampire? Um... No again. JK Rowling's beast would paralyze or kill any vampire and make it cry. Harry Potter wins. Always. Forever
When I think of Vampires I think needy and lazy. They hang around for potentially forever contributing very little and changing nothing.
For example. Why don't vampires have to work on bettering themselves? As a human adult you're expected to work on improving yourself. To be happy. To be grateful. To be calm. Yet the older vampires get the more self entitled they become. They nest all day and dress immaculate at night. Dying by vampire would just be annoying. It would be late you'd be tired and now you had to deal with vampire theatrics.
Match night between Vamp and Baz-
Vampire meets Basilisk. Vampire can't help but harping on about their shiny raven hair and rare collection of sex slaves. Vampire begins to feel tired as tank is low and needs to sits down. Basilisk looks at vampire. Vampire dead.