Hey Chawk,
Not sure exactly of the differences in the story...but...."New Spring: The Graphic Novel" is basically a set of comic books based on the real "New Spring" book. So, the graphic novel has lots of artwork and a different writer to boot. However, the stories in the graphc novel's pages are based on Moiraine's and Lan's adventures. Adventures that took place leading up to the start of The Wheel of Time.
I haven't had the pleasure of reading any of the graphic novels...but, I've heard good things about them.
Hope this helps!
-Garrison Bain-