I haven't knit with the KP Organic yet, but I have a skein on the way!
My experience with cotton is that I hate using wooden needles with it. It doesn't slide very easily for me. I'm a bit of a tight knitter.
Also, cotton is not as "elastic" as many of the acrylic yarns I've worked with, unsure about rayon or nylon. In fact, cotton is very INelastic. What you knit is what you get with almost no stretch.