I think that my favorite Edward's are in tune with some of my favorite stories, tbh.A Pound of Flesh
has a great Edward, rough around the edges but ultimately good to his deepest core and I love how he loves his Peaches.Starry Eyed Inside
has an Edward across several years and many different sides, so you're almost sure to enjoy at least one facet; I love them all, but then it's one of my all-time favorite stories
*sigh* so many Edwards, so little time. But those are the first to come to mind when I read your question.