Maybe it comes down to semantics, as is so often the case.
Immersion, for me, is about forgetting that I'm playing a game and feeling like I'm taking part in the fantasy.
For whatever reason, that's easier to achieve for me when I'm not looking at a party or an avatar - because I'm the sort of person who identifies with my actions in a game. I don't "act the character" - I act myself, as the character - if that makes sense.
Which means party based games are significantly less immersive to me, even if they're using first person perspective. Unless, of course, it's a party based game where I'm clearly the protagonist and I just have some followers - though I definitely prefer solo games for immersion.
So, the perspective is just part of the equation - and I'd say games like The Witcher or Risen are more immersive than Grimrock or Might and Magic - because I'm just one person.
But for "ultimate" immersion, I'd have to point towards first person games, including System Shock, Thief, Bioshock Infinite, Skyrim, and so on. Even though a game like Risen can be extremely atmospheric and immersive - it doesn't QUITE make me feel part of the fantasy on that same level.
That said, I must admit that Dead Space did manage to scare me and make me feel part of the world unlike most third person games. So, maybe the perspective isn't quite as vital as I think it is. However, the camera view IS kinda untraditional in DS - which might be a factor.
Another big factor is the premise and the setup of the game. Some games excel at building up tension and creating a scenario that I can easily lose myself in - where as some games just dump you in the action without making you care.
Bioshock and Bioshock Infinite are both games with EXTREMELY strong premises - making them extra immersive.
The first Gothic game was also particularly powerful in its premise, and it was very easy for me to identify with the concept of that prison colony - and they did a fantastic job of setting up the various camps and characters. So, the first Gothic is probably the strongest, for me, when it comes to immersion.
Beyond that, it's vital for me to be the "author" of my character as much as possible. I'm taken out of the game if I have to play a well-defined character, and The Witcher is a pretty good example of that. Sure, the world and the atmosphere are both very strong - but Geralt is a very defined character, and it's harder for me to lose myself in that world because of that. Thankfully, he's a character that I can identify with - but it would have been better for immersion if I got to create my own character.