I have both. Initially, I looked for something I could get up and running quickly, easily, and inexpensively. So I went with Blogger for the blog, and Google Pages for the website.
Both met my initial requirements. I continue to be pleased with Blogger, but now it's time for me to find a more flexible solution for my website. It's perfectly functional, but not especially attractive, and I'm limited in what the template will let me do.