As you've seen Zack Snyder's Man of Steel has a very cool, and unique Superman logo that I think is great. Graphic designer Dave Jones has taken the look of that logo and given each of the other Justice League team member a new logo design inspired by the one we've seen for Man of Steel. Here's a statement form the artist to ComicBook.com...
These Justice League logos are inspired by the “Man of Steel” movie. The Superman (Man of Steel) logo is my best attempt at replicating the movie’s poster featuring the stylized logo. The Batman (Caped Crusader) logo has three separate bat images on different depth layers. I intentionally did not use the Dark Knight logo for this one. The Wonder Woman (Amazon Princess) logo is a combination of the classic design with the New 52 style. The Flash (Scarlet Speedster) logo includes glowing elements and speed lines. The Green Lantern (Emerald Guardian) logo also includes several glowing inner layers. The Hawkman (Winged Warrior) logo has yellow straps connecting the outer ring to represent his chest emblem.
I think they all turned out really cool, and he's currently working on one for Aquaman.