The second video may give us our first indication that Superman - or something else - is involved as it looks like the extras are looking up at something.
It's unknown specifically what the scene is about or where it takes place in the movie, but we can speculate the destruction is obviously not involving Batman, as we see Bruce Wayne actually making "saves" without his costume.
It's possible that Superman could be battling something or someone (Doomsday?), which causes the destruction of the Wayne Financial Building, and perhaps gets Batman to notice.
Could this be the opening scene to Batman Vs. Superman? Zack Snyder did have an action-packed 15-20 minute opener for Man of Steel with the Krypton scene. He's going to need a big one to top that.
"Batman v Superman: Dawn of Justice" has a March 25, 2016 release starring Ben Affleck as Batman, Henry Cavill as Superman, Gal Gadot as Wonder Woman, Amy Adams as Lois Lane, Laurence Fishburne as Perry White, Diane Lane as Martha Kent, Jeremy Irons as Alfred, Jesse Eisenberg as Lex Luthor, Ray Fisher as Cyborg with Callan Mulvey, Holly Hunter and Tao Okamoto in new character roles for the film. Justice League is to follow directed by Zack Snyder as well.
For more news on the "Man of Steel" and related movies head on over to the Cosmic Book News Superman movie hub.