Sorry. I've never found Capote to be an important writer. "In Cold Blood" was a horrifying tale, in which he previewed the liberal obsession with identifying with the murderer instead of the innocent family which the two bums butchered. Look at Norman Mailer's defence of Gary ? who was released and then committed more murders.
Harper Lee's work was a little more refined, but I must plead ignorance, having only read "To Kill a Mockingbird".
All crime writing, from its start, always focused on the perpetrators and their crime(s)rather than the victims. You're looking for political motivation/pathology where none exists. Capote, for his part, was afraid and appalled by the act portrayed in In Cold Blood. However, he broke new ground in the way that he told the story. At the time, Mailer was one of his most outspoken critics, then later copied the style with the Gary Gilmore book, Executioner's Song.
Also, most people forget that Capote was at his core a "country boy" and particularly well-suited to tell the story. As it turns out, he was singularly unsuited for NYC and the environment he aspired to and eventually found himself in. Most people remember his "queer act" from television talk shows and public appearances. I saw him once, a few years before his death, and his manner was entirely different. The voice was at a lower pitch and the fluttering hands not in evidence. He was discussing a book in detail and seemed to be "all there," but sickly.
Harper Lee only wrote the one book, but for millions of school children it's the book that has served as their introduction to modern American literature
p.s.
You could make the argument that Capote's Breakfast at Tiffany's, The Great Gatsby and O'Hara's Butterfield-8 are essentially companion pieces. If you read all three at the same time, it's difficult to tell which is the best told story.