This has been done to death, but my perspective (which is correct
) is that neither TPP nor FPP are necessarily "more immersive" in and of themselves.
What it is, is that FPP is "more immersive" in situations where you're scared,
because it mimics tunnel vision.
TPP, on the other hand, is more immersive in most other situations, because it mimics 3-d situational awareness (which is built up out of subtle environmental cues, particularly audio, and the constant saccading your eyes normally do, all feeding into an internal model in your brain, of you as a 3-d object in a 3-d world). If you think about it, your normal sense of "me" isn't that of a you being a viewscreen or a window, but (again) of a 3-d object situated in a 3-d world (although there's an interesting side-light related to what's been called "enlightenment" in this, but it's too far afield).
So really, ideally you want to be able to switch. If your character is in a situation where they would be scared, then FPP is the way to go - for example as you're inching through some dark, gloomy dungeon. But in most normal circumstances when you're out and about in the world, TPP really glues you to your character more.