I'm not sure they do it uniquely, honestly. So much paranormal detective stuff falls back on the same three tricks: the heightened senses reading the scene like a neon sign, the immortality giving them historical context, and maybe some mind-influencing power to get info out of people. It's a cool premise, but the execution often feels lazy. The real distinction for me comes from how the vampirism complicates the investigation. A detective who has to avoid daylight or can't enter a home without an invitation? That's a logistical nightmare that could be fun. One who struggles with the scent of fresh blood at a crime scene, fighting their own nature while trying to analyze it, adds a layer of tension most procedurals lack. 'Midnight Riot' by Ben Aaronovitch does a better job with a magical apprentice cop, I think, because the magic system has rules that interfere with police work.
What I'd love to see is a vampire detective whose solution hinges on a cultural nuance only someone from a different century would spot, but not in a cliché 'I knew Napoleon' way. More like recognizing a folded prayer in a victim's pocket as specific to a heretical sect thought extinct in 1792. The supernatural condition should create unique obstacles and insights, not just be a power-up.