The videos in the trailers are the same, but the voice-overs are different. The first one (The one you'll probably see with Batman) features the voice of Russel Crowe AKA Jor-El. The second trailer features the voice of Kevin Costner AKA Jonathan Kent. Kent's speech is much more about choice, making it clear that he understands that Clark could potentially be a villain. Jor-El's speech embodies much more of Clark's fate as the hero of Earth and the Last Son of Krypton.
Overall, I like the trailers. They aren't really what you'd expect from a Superman movie, but the speeches are revealing even if the clips aren't. Looks like a cool take on the Superman legend. Man of Steel fly into theaters in June 2013.
P.S. Yes, that is music from Lord of the Rings.
P.P.S. Is that Krypto, the Super Dog?