I prefer third person shooters. However, my reason isn't because of the gameplay, because I feel first person shooters have better gameplay. I like third person shooters because I feel like it adds to the story. Unless it's games like Fallout, Elder Scrolls (Not even a shooter but whatever), or any other games where you are the character and you choose their path, I feel that third person adds more to the story. With games like Fallout, you are the character. You are in control of their emotions, morals, relationships, decisions. Being in first person helps with the immersion so you actually feel like the character instead of some avatar. Which I feel like is more of a gameplay thing than a story thing. The gameplay involves you setting your path and feeling like the character, but the story is detached from that mechanic because it's told through your actions and decisions. However, in games where the character is set in stone with a set path and set personalities, the first person takes away from the bond with your character. You never see their face, so the connection with the character feels lost and vacant. It's like you're the character, but you're not. You're only looking through their eyes and experience things around them instead of experiencing them as a character.
Now, I do like the non linear gameplay and the feeling of choosing your own path that games like Skyrim give you. The games that immerse you and make you feel like you're part of the world. But I do really love the story driven games that put you in the action of the story instead of just telling it to you. I feel like, story-wise, Bioshock would have been better third person because you never see the characters you are playing. The connection is lost because instead of seeing the story and scenery around them, you are seeing it as them. Which takes away from that character, the main character, at least in my opinion. Mass Effect is the opposite though. You are the character, but you are seeing thing around you. You are playing as an avatar, but you're them. You make their decisions and carve their path. This is why first person is better in this situation to immerse you.
That probably doesn't make sense, but I really do feel like in games that don't involve you carving your path and are giving you a story to experience. Third person is just better for the experience, and I really enjoy games that tell you a story by putting you in the action and showing you the main character that you are supposed to grow attached to. With first person the attachment is lost because you're playing as them which makes you feel like you are the character, but you're now.
So, story-wise, third person is better, but gameplay-wise, first person is better.