That's highly subjective and depends on how you approach the medium you're "immersing" yourself in. I, for example, was more immersed in Fallout 2 than 3. And infact, due to the "immersion" factor, I'd go as far as to say that the combat, to me, felt more "realistic" (if that's the word we have to use) in Fallout 1 and 2 than in 3. But as I said, a subjective matter that depends on how you approach it. Similiarly I was more immersed in Steel Panthers than Close Combat or C&C, and more in Operation Flashpoint than Bioshock.
Immersion > as in deep involvement, (dictionary).
How deeply you are immersed in a game is, of course, dependant on how much you like the game.
However, you cannot immerse into a certain aspect of a game,
at all, if that aspect is not actually present in the game. Turn-base play, if not there, you cannot immerse into it.
Turn-base, if only occurring once or twice in the game, will have a lower immersion possibility as well, the more there is, the more immersion.
Same with any role-play aspect, if there is a lesser degree there, then the immersion possibility will be less.
If playing the role of a person walking in a role-play game, there would be a higher immersion possibility in that role-play, if the animated action was realistic than if of the TB less realisic movement.
That's the compromise and loss in those having board-game type movements.
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Turn base play requires pre though out play, but normal real-time play also has pre though out play. Real-time play, it's sequence of actions and responses are, or should be, pre considered, as in real-life battles and military training.
Once you've been in the game a bit, in effect training, turn-based-play actions will become a bit repetitive and need less thought. The same happens if playing real-time, the actions, movements and responses are already familiar to you.
It was like that in Fallout Tactics when I switched to turn base play for a bit, it was a drag having to play out, step by step, the movements and actions that I would have done in real-time anyway. I switched back again.
Sure, TB is fun figuring it out, and very satisfying to see your calculations play out to a win, but it can wear off a bit as calculations become much the same and familiar to you, as it does in real-time as well, even my real-time combat actions have become pretty automatic. Turn-based play would have dragged it out much longer, and were it in Fallout3, I would have switched it off, way-back.
Just pointing out some pros and cons.