Differences in the way they play

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).

It might sound strange, but Wikipedia and/or the 40k section of the (unofficial but rather thorough) Lexicanum seems like a good starting point to get to know the setting. :)