I've made more log cabin quilts than anything (one even won an award at a quilt show), and I paper piece them. I don't have to worry about squaring up, make them 5 or 10 at a time, while watching a baseball game or something. My favorite part about paper piecing is not having to pay that close attention --- just have to remember my lights and darks, and that's it.
BTW...Great string quilt Peckish.