I only read the first arc of Green Lanterns and a story in one of the holiday specials but I really, really like what I've read of Jessica. A Green Lantern with Generalized Anxiety Disorder is the sort of I-can't-believe-no-one-thought-of-that before genius that only Geoff Johns could come up with. I mean, I'm ambivalent about Johns in general (sometime love his stuff, sometimes really hate it) but he's a master at this sort of thing and hats off to him for creating such a great character.
By the way, does Green Lanterns get better? I loved the characters - or Jess, at least, I only started to come around to Simon by the end there - but man was the plot boring in the first arc. Though, to be sure, it might just be that I'm utterly sick of the bloody Rainbow Corps (another great Johns idea that was unfortunately beaten to death years ago) but it was massively decompressed and not all that interesting to begin with.