I like both story and characters. You can have a good story with shit characters. See SAO. Very two dimensional, but I enjoy the story nonetheless.
When looking at a story, you look more to the events than the characters. When looking at characters, you look more at their individual quirks and their individual in-depth stories of hardships and triumphs.
I like Lightning as my 10th pick because, let's face it, I was running out of characters. And she's one of those characters I feel has potential if her character was given more effort.
Also, I like the way she looks. That's kinda it. And that I like her fighting style in Dissidia 012 Duodecim FF.