Dark Heresy is probably the most similar to a traditional game in this regard. Because there is no default status quo, you can pretty much go in any direction imaginable without significant hand waving.
Rogue Trader does tend to lend itself to games that have some space combat/travel/exploration component in order to allow all players to contribute (not quite as bad as deckers in Shadowrun, but a similar problem).
Deathwatch really and truly seems designed for episodic play (though you could easily work in overarching plots). A lot of the rules necessary for longer play (insanity and corruption in particular) are very weak and not well developed and the mission-based structure essentially gives you the format for each episode.
Any reason to recommend one over another
I think each game really does bring something unique to the role playing experience. To some degree, these answers are quite subjective and could be modeled in other games, but the rich backdrop of the 40K universe really helps drive these elements home.
Dark Heresy - Really encourages the exploration of the mythos and gives a GM a lot of opportunity to develop deep, intricate (perhaps even obtuse) plots with encounters that seem truly lethal and require cunning and skill to get through. [rich skills, winding plots, lower power level increases lethality]
Rogue Trader - Out of the systems, this is the most interesting in a lot of ways in that it delivers on the promise of roleplaying in a Star Trek style without that silly Prime Directive. Players are fairly powerful and masters of their own fate, each highly specialized with something to do. Combined with the geeky attraction of designing your ship, I think this game has quite a bit to offer. [Star Trek-style exploration, deep character specialization, ship design!]
Deathwatch - For many, this game will be the winner simply because it's Space Marines. While it does lend itself to combat-intensive sessions, FFG has done a good job of trying to give the marines some actual personality (although this personality is often hidden and only revealed in the solace of their own rooms). However, the mission structure has a similar appeal to the job layout of Shadowrun games and can really help get players moving. And of course I would be remiss if I didn't mention the very detailed combat mechanics and options which do allow for some fairly cinematic gameplay. [roleplaying hints for players, clear session objectives, interesting combat]
Any with a more enthusiastic following than another
I think it's safe to say that Dark Heresy has a larger following, but this is a factor of age. Otherwise, I think the vibrancy of all three games is pretty light outside of Fantasy Flight Games' own forums (though I did notice that the Deathwatch forum nearly has as many posts as the Rogue Trader forum at this point even with the year head start the game had, so it may be that Deathwatch will end up being the more popular game).
OK, I don't have time to answer this as I want to. My background is in psychology, and I fell into role playing games when I turned 10 in 1976. So by the time I was in college, understanding where the term Roleplaying game really came from, I understood the critical nature of immersion, how it is the most important ingredient for game success.
And to be clear, the definition of immersion is to "Immerse oneself into the identity and Role of the part one is playing. To respond, as much as possible, as the person one is playing, not as oneself."
And before getting into the smaller details, I will dive right into the fact that the very system/game one chooses has a huge amount to do with the amount of Immersion.
Metagaming is the opposite of immersion. You use both terms, but I need to make that absolute definition from the beginning. This also means rules that encourage metagaming decrease the immersion in a game and therefore, decrease the main ingredient of a roleplaying game. The mechanics are called "Dissociated Mechanics", a term coined by Justin Alexander. This is very worth reading, because it gets into many of the larger picture issues with players being able to use in-game logic to see the world around them, as opposed to the rules forcing dissociation from in-game logic.
Once the players assume that rules are going to determine the content of an encounter or treasure (based on EL, or whatever) instead of what the environment or history of the area dictate, verisimilitude is lost.
Vreeg's Rules of Setting design are also heavily immersion related. My current campaign is 26 or so years old (started in '83). Building verisimilitude is a huge part of this.
Vreeg's first Rule of Setting Design
Make sure the ruleset you are using
matches the setting and game you want
to play, because the setting and game
WILL eventually match the system.
Corollary to Vreeg's First Rule
The proportion of rules given to a
certain dimension of an RPG partially
dictate what kind of game the rules
will create. If 80% of the rulebook
is written about thieves and the
underworld, the game that is meant
for is thieving. If 80% of the
mechanics are based on combat, the
game will revolve around combat.
Multiply this by 10 if the reward
system is based in the same area as
the preponderance of rules.
Character growth is
the greatest reinforcer. The
synthesis of pride in achievement
with improvement in the character
provides over 50% of the
reinforcement in playing the game.
Rules that involve these factors are
the most powerful in the game.
Vreeg’s Second Rule of Setting Design
Consistency is the
Handmaiden of Immersion and
Verisimilitude. Keep good notes, and
spend a little time after every
creation to ‘connect the dots’. If
you create a foodstuff or drink, make
sure you note whether the bars or inns
the players frequent stock it. Is it made
locally, or is it imported? If so,
where from? If locally made, is it
Vreeg's Third Rule of Setting Design
The World In Motion is critical
for Immersion, so create 'event
chains' that happen at all levels of
design. The players need to feel like
things will happen with or without
them; they need to feel like they can
affect the outcome, but event-chains
need velocity, not just speed.
Vreeg's Fourth Rule of Setting Design
Create motivated events and
NPCs, this will invariably create
motivated PCs. Things are not just
happening, they happen because they
matter to people (NPCs). There is no
need to overact, just make sure that the
settings and event-chains are
motivated and that the PCs feel
Vreeg's Fifth Rule of Setting Design
The Illusion of Preparedness is critical
for immersion; allowing the players to see
where things are improvised or changed
reminds them to think outside the setting,
removing them forcibly from immersion.
Whenever the players can see the hand of the GM - even when the GM needs to change things in their favor -
it removes them from the immersed position.
(Cole, of the RPGsite, gets credit for the term).
Remember that part of immersion is the lack of feeling walls around and rails under the characters. This means that the players should not feel that there are things that their character cannot do solely because of the rules or the GM's mindset. The job of the GM is to enable roleplay, not to inhibit it.
This also means the GM must be as immersed as the players, or more.
Another big-picture thing that may irk some folk who sell stuff is that published settings can hurt immersion. They don't destroy it; but when the players have a lot of knowledge about a setting that their character would not have, this increases the opportunity to use it, consciously or unconsciously. Similarly, if your setting has its own bestiary that the characters learn as they go along, or at least a lot of homebrew tweaks, the players get used to working with the in-house data and not trusting the published sources.
If you have done all of this larger-scope stuff, the smaller scope stuff becomes easier. As a GM with miles on the tires, I find that playing up the level of knowledge my NPCs might have and do not have helps keep the players in the same mindset. Players key heavily off the way the GM plays their NPCs. They won't do the funny voices or the mannerisms if the GM does not, and if the GM is particularly careful about what their NPCs know and don't know, especially verbally, the players emulate this.