I get better immersed into third-person games, because they generally have better stories, and I'm a story kind of guy.
With a third-person perspective, things can get more cinematic. (Let's be honest, first-person cutscenes don't have nearly as much room for variety.) Also, I'm playing as someone that isn't me, so of course that character can do the things they do. Cole McGrath can shoot lighting out of his body. I cannot. Sora can mow down legions of Heartless. I cannot. So on and so forth.
In a first-person game, it's implied that I'm the one performing these actions, but I know that there's no way in hell that I'd ever be able to take down a Super Mutant Behemoth in Fallout 3, or wreck a Big Daddy in BioShock. (Though really you play as Jack in BioShock, not yourself.) This causes extreme disillusionment for me, and unless I'm having a shitload of fun, I probably won't play a first-person game for as long at a time as I might a third-person game.
I guess it's really a subjective matter, but I think third-person is way more immersive than first-person.