The harshness of the compression is similar to API's boxes. It might be one, although I never can remember the number of model.
The cool "damaged" sound are most certainly an artifact from (very likely Cedar) noise-reduction, EQ, and probably a mild distorsion to make it pop in the trailer. It's pretty safe to say it will sound different in the final film.
To truly reach this effect, you'll need good gear/mics with a clear lower mid (no mud), the acoustics under heavy control, and a voice that can actually perform this. The character of the voice is all in the lower mid here, which is what makes it sound "sctratchy" and nice instead of distorted.
Mind you though, I have no clue what exact kind of distortion is used. I'm guessing here (based on listening through YouTube on my home HD650-headphones/Prism interface/ancient i7-computer), but either they have some kind of modeled plugin i'm not aware of, or they've been using some kind of (quite possibly valve) analogue signal-path, which was overdriven to reach this very goal.
Myself, I'm about to try out tops from Vox and Marshall (to begin with) just for this very reason. For the moment, my trusty reamped old modded Boss DS-1's does the trick for many applications needing vicious bite, but they're hardly subtle, even on low settings.
Right now, my money's on the Vox-top, based on a combo I've been working with a lot a few years ago, but the jury's still out. Awesome mid, it has!
Well, no matter which it is in this trailer (be it software or hardware), the lead word here is "moderation". Make the voice pop in the mix, but don't let it sound actually damaged.