Standard-issue giant monster would be fine with me - I don't have a lot of demands from the genre, and they've already nailed two of them quite nicely.
The thing about the trailer that I keep coming back to is the brief sound at the beginning of the first "roar", where the lights first flicker. There's something compelling about it in a dreamlike way - more like a feminine voice saying something on the edge of intelligibility than a monster's growl. It reminds me of a sound that wakes you from dreaming: you know something prompted you out of sleep, but as you become aware that you are awake, the sound hangs like an echo on the edge of your conscience - significant, yet unresolved...
It's very interesting sound design, and the main element that suggests to me something slightly more along the lines of a Cthulu than a Gojira. It looks like it'll be fun to find out, either way.
I also find it interesting that Abrams somehow managed to get more of a sense of scale into a handheld-shot trailer than Spielberg did in nearly all of War of the Worlds*, and did it using the same tactic of keeping the action with the (ostensible) protagonists.
*I enjoy WotW, despite flaws - probably because it also meets my admittedly soft genre demands.