I will always prefer first person perspective in games. It is more immersive for me, because I can feel like I'm inside the game world more easily. When playing a third person game I cannot stop thinking that it's not "me", it's the player character doing shit. I will never fear for "my" life in a third person game the same way I would in a first person perspective.
Whenever a game allows to change the view I will always select it. I got interested in GTA only after GTAV release got the first person view (well, I liked GTA 1 and 2, played some of Vice City). I'm going to play RDR2 exclusively in first person mode. I played all Bethesda games in FPP too. In third person games there is often a moment when the camera cannot fit behind the character and will move to a view that's pretty much first person. That's when I have to stop playing for a while, because I'm suddenly more immersed for that short moment and ripped out of the immersion the moment later. This happens the most in Divinity 2, it happened a few times in Elex during my recent playthrough.
I am much more immersed in games with a top down or isometric view than third person. Looking at the character(s) from above is easier for my mind to comprehend than watching the world through an out of body experience, following "my" body around, looking at its back. The thing that make me immersed in isometric games the most is the audio - the music in Fallout 1 & 2, the music and ambience in Planescape: Torment and Icewind Dales are the best examples that come to mind. Pillars of Eternity 1 almost nails it too.
So, to sum it up: a 3D game with first person perspective is more immersive to me than a third person perspective game. I understand the limits of FPP (narrow field of view, sometimes problematic melee fighting), but the limits of TPP are more annoying to me (seeing my character all the time, not being able to look at items within the game world because they are obscured by the character, not being able to fully care about survival). I'm currently playing Pillars 1 and I'm enjoying every second if it and I feel more immersed in it than when I was playing Elex a few days ago.
PS - the most annoying kind of third person games are shooters. Each and every shooter with TPP I see I always think to myself "damn, I'd play this shit if it was in first person". Pretty much all of these games have the player character a little bit to the left of the screen, just so they do not obscure everything completely and when the gunfight starts, the view zooms in to pretty much the same field of view an FPP game would have, just instead of the weapon model in the corner of the screen, you see an arm and a part of the head of the character. And when you stop aiming, you get dragged back again.
PS2 - with all the issues I have with third person view, I do enjoy games like The Witcher 3, Elex, the Gothics, etc. It's just... I know I would enjoy them even more if I could change the perspective. I do understand, though, that if a game is designed around TPP it is not always possible to just add an FPP view (and vice versa) with just a few tweaks in the code. I get it that the combat model of the Wither 3, for example, would not work in first person.