Arrow of Slaying +3 (undead) vs. Vampire

Which of the specifics holds sway in the text? I know that under vampires, it specifies how they can be destroyed, but the slaying arrows say the hit creature is instantly killed.
I assume that if you shoot a vampire with an arrow of undead slaying, they are not killed, but transformed into their gaseous form and can reform in their nearest coffin 8 hours later. But maybe the slaying arrows are an important loophole.

I’d treat it as a stake to the heart. The vampire is paralyzed and powerless. Beheading it will finish it off.

Thanks. That’s helpful. I’m working up some motivation for vampire-given quests, and destroying arrows of undead slaying is one of them.