To me, quiet books are NOT synonyms for literary books or character-driven books, as opposed to action-oriented or plot-driven books.
To me, any book dealing with DEATH (particularly of someone young) is NOT a quiet book. The Diary of Anne Frank and Bridge to Terebithia, etc. are NOT quiet books to me, although very compelling in their own right. They're just too darn sad.
A quiet book to me is like comfort food. They are either lightly funny and upbeat, or soothing and peaceful. They are always gentle. These kinds of books have timeless appeal either b/c they're just right to share with a child at bedtime or to they can pick you up from the doldrums and put a smile on your face.
Examples for young children are the Little Bear series (yes, Sam Hranac and Inspiration!) and Jesse Bear series and Big Bear & Little Bear series [e.g. Can't You Sleep, Little Bear?]and Frances series [e.g. Bread and Jam for Frances].