It's a hard question to answer. Games can be scary in 1st person, or 3rd person - yet, they're both unique game formats, and needed to be treated differently.
I think if you're designing a 3rd person horror game, it's important to make the player care about the character they're controlling. It's like a horror movie. If you don't care about the hero, why would you be scared when s/he is in danger?
Personally, I
LOVE FP games, and I find them much more engrossing than TP games. That's why I think they're scarier (for the most part).
Either way, you need only ONE thing to strike fear into the heart of the player:
Make them feel vulnerable.
I love an enemy that I know can kill me with 2 or 3 hits. It's so much scarier. Also, create lots of random encounters - that way, if someone plays your game 2 or 3 times, new surprises will hit them each time.
Narrow passageways make me tense, especially when I do end up fighting something huge.
I freak myself out easily while playing games that are
dark, cramped, changing, disorienting, and unpredictable.
Hope you find this post insightful!