I'm not falling for hacks like J.J. Abrams stuff anymore. He sells people on not showing you anything at all. The payoff is always not very good. Monsters looks like it's along those lines to me.
Monsters is actually supposed to be more of a love story as the main part with this sort of monster attack aspect layering over it. Its not going to be anything like District 9 or Cloverfield. I know the trailer makes it look like that, with a lot of action sequences, but its actually the opposite. It's supposed to be a very slow moving, emotionally driven movie with a few action scenes of course. To me, it seems like a very unique movie. Not anything like those JJ Abrams type movies you're mentioning.
And it seems as if Stone is going to bomb. It has terrible reviews so far, which is too bad because of the two great actors involved. It has something like a 40% on RottenTomatoes.