I find third-person allows you a better sense of where you are, thus making it easier to avoid shots, enemies, hazards, etc. That's not as easy in first-person.
In open ended environments, until you reach tight and claustrophobic areas, that's when the camera tends to conflict with the character and how far/close you're able to view it. I've played a myriad of 3rd person games, where the camera either has to go out of focus of the character in tight spaces, or simply clipping into the character, while still tying to give you a view of what you're looking at.
This is hardly a problem for first person games, due to the fact that you're the camera, and the only possible character modelling that could get in the way, is either the hands, or the weapon models being made absurdly large (like Fallout games to a degree as one prime example, or the latest Wolfenstein/DOOM games (You can even find old Total Biscuit videos, where one of his major complaints of some games he's reviewed critically, can involve rather large weapon models, that obscure him being able to view anything properly).
I've still found myself at odds with third person games, mostly thanks to cover mechanics and the lack of fully versatile movement. In first person, you literally just hide behind an object of your own free will and peek around yourself, without having to press a button to do it yourself. Third person fully manual cover movement isn't entirely as precise either, thanks to parts of your character popping out of cover, or you having to really fidget around with the controller/kB, to really get your character into proper position (I'm talking near the edge of objects, not fully in the middle of a massive object, which anyone could do, due to the size of the object itself).
Again, I don't see third person holding superior sway over first person. Third person is you just looking at the character from a panned out view, an "out of body experience" if you will. Immersion wise, that doesn't always fit well with every single game, while with first person, you are that person, because you are looking from their viewpoint, and not watching them from a panned out camera.