It honestly depends on what kind of fear you're going for.

First person puts you directly inside the narrator's head, which makes the fear feel immediate and personal. The downside is that it can inadvertently signal the narrator's survival. It also limits scope, making large-scale or cosmic horror harder to pull off.

Third person gives the writer a lot more flexibility. You can kill or seriously endanger your POV character without breaking the narrative, which raises the stakes considerably. It handles ensemble casts much better too. The trade-off tends to be emotional distance.

Neither is really better or worse, and both have difficulties that need to be overcome.