Shocktillyoudrop.com and Firstshowing.net are live blogging from Hall H and they have descriptions for the new Godzilla footage. What's important is that director Gareth Edwards stressed that the film would be take itself quite seriously. It was also implied that the teaser won't be put online for quite some time. Bummer!
The narration is from Robert Oppenheimer. "We knew the world would not be the same. Few people laughed. Few people cried. Most were silent. I remembered the line from the Hindu scripture. The Bhagavad-Git... takes on his multi-armed form" (This is were we see the other, dead creature)
"And says, 'I am become death. Destroyer of worlds." That's where we see Godzilla's face and the logo
That's the narration in the trailer. It's a Robert Oppenheimer quote about the atomic bomb.
We see the side of something huge, like a mountain. We only slowly realize it's actually a monster. There is something like lava running down the side of it. And then there are huge CLAWS. The monnster is laying on its side. There is a huge Godzilla scream! Like a massive trumpet sounding!
And then Godzilla is rampaging through the city, trashing buildings with its huge claw. Buildings collapse. THOOM. A giant arm swipes across the city and everything crashes. We see its massive spiky back and then the trademark face. The monster opens its mouth and SCREAMS. - io9.com