A major complaint of Man of Steel was Superman breaking Zod's neck. Now Bad Ass Digest is stating a scene in Batman Vs. Superman will have Superman confronting a bad guy saying, "I won't snap your neck, I'm going to take you to prison."
However, the report also mentions that Superman "loses his cool" and threatens to break someone's back.
Another complain of Man of Steel was the fact the battles took place in populated areas (though Superman didn't really have a choice), It's said that during a fight with Doomsday, General Swanwick says that Superman will lead Doomsday away from populated areas "because he's a hero."
While the dialogue does sound super cheesy, it's noted the script they got the rumors from may have been old/unfinished.
Other rumors include that Batman Vs. Superman will start off with Batman's origin story, and then show Bruce Wayne going to Metropolis during the Superman vs. Zod fight from Man of Steel.
It's said the movie will take place a couple of years following Man of Steel; Lois and Clark live together; Clark would rather cover Batman stories than the Metropolis vs. Gotham City football game; Superman saves Lois when she is on assignment in a foreign country, which causes an international incident as other countries view Superman as a tool/weapon of the United States (China apparently has banned Superman from their air space); most people support Superman except Lex Luthor and a "cautious" Batman who is developing anti-Superman weapons.
"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.