While I can understand that draw, I find psychological horror a poor choice for campaign play.
It's a matter of how to pull it off, not inability to do it. Plus, many "horror" games are merely survival games with ugly threats...
See, this is part of the thing - the game is fundamentally incapable of generating a horror reaction. The rules can't do that. The horror has to come from the GM's presentation, and your own ability to play into it.
Sustaining that for campaign play is hard.
the thing is, a game
can sustain a psychological horror feel via mechanics, but only by the players knowing some deep dark fate awaits them via those mechanics.
WoD just isn't good at doing that kind of thing. Alien is.
oWoD winds up being a warped form of supers or slasher flicks in most hands, because the mechanics for Rötschrek are weak
and often ignored. Plus, it's always temporary; Alien & WFRP 1, the essential campaign question is "Which gets you first? Insanity or the Enemy?" In both, PCs wind up with a slowly accumulating series of disabilities... Pendragon can result in similar, albeit more player control, with passions... especially hate and fear passions (which can override the Valourous/Cowardly trait pair... and each other).
When one is playing behaviour limitation roulette with a character one's fond of and attached to, it's a good bit of stress on many a player.
oWod lacking a lasting effects with mechanical impact meant it didn't' generate the sense of impending doom that Alien, WFRP 1, or even a harsh game of FFG's Dark Heresy will. When, not if, will your character buy it, and how? Insanity? Mutation? Eaten alive? Ripped apart?
What I've seen of the newer editions (CoD/nWoD) doesn't seem much different from oWoD on that score.
I like the VtM 1E mechanics, but not so much the later ones. I've actually run more of the StreetFighter RPG than any of the other Storyteller games. (2 campaigns, about 50 hours of play each, plus several one-shots.) But none of them I've run (V:tM, M:tA, V: DA+Sorcery+Mummy 1E) generated horror for the players. The VtM one generated horror for a non-playing observer, tho'... (None of us realized her phobias were being triggered until after session; heck, we didn't even process she was present until after session.)