I've talked a little about choices, and in the rambling nature of my discussions, we shall alomst certainly return there. However, this post is about immersion.
There is a theory that states that roleplaying is divisible into three overall philosophies, and all RPGs will contain aspects of all three, and fall somewhere in a triangular chart between them. Likewise, all Roleplayers will have a sweet-spot on that same triangle.
The three philosophies are:
Gamism is about the system. It's about balance, fairlness, playing challange, and-a lot of the time- the stats.
Narrativism is focus on storytelling, with a fair chunk of the characterisation involved.
Immersivism looks towards the convincingness of the player experience. Both in the ways the system allows for interaction, and in the audio-visual-tactile presentation of the setting and characters.
When looking for examples, one could say that Bioware tend towards the heavily narrativist, with a substantial quantity of gamist level balancing, 'ability' use, and stat tweaking, and less focus on Immersivism. Although with the Mass Effect series they seem to be balancing out the last two, while keeping their narrativist focus.
The Elder Scrolls and Gothic (disregarding Gothic 4) series both seem to be aiming (with varying degrees of success) for a fairly even balance.
Interestingly though, it's quite rare for something billing itself as a CRPG to focus on Immersivist philosophy except in terms of graphical quality. The Mount and Blade games do, to an extent, but that's about it.
To find true Immersivism, one often has to look outside the official boundaries of the genre.
For example, Grand Theft Auto 4 is not billed as an RPG, yet even without the first-person-POV mod which I use to truly immerse myself in Liberty City it has a great deal of Immersivist roleplay.
Note that you, the player, never get any dialogue options, Nico will say what he says in the script, Nor are you presented with a huge number of options about accepting 'quests' and how they pan out, although ignoring the plot seems like a viable option (I'm not in my playthrough, I'm really rather enjoying the story), which gives you... actually as much if not more control over the plot than most JRPGs at least..
Where you do have a lot of choice is in protagonist Nico Bellic's day to day activities and his relationships with the people in his life. As Nico, you can kill an afternoon in your flat watching (hilariously satirical) TV, you can invite a girl out on a date, hang out with your idiot cousin, go drinking with friends, take in a show, find honest work buy clothes, go for a walk or a drive around the city, mug an old lady in a dark alley (it's a GTA game, after all). You live the chracter's life, in a vast and somewhat realistically presented 'living' city. That's immersive.