The big difference, as far as SEO is concerned, for a subdomain blog (blog.) versus a directory (/blog) is how the link credit is attributed. Search engines see a subdomain as a completely separate site. Any backlinks you get to your blog content will only benefit your subdomain blog. When the blog is a directory it is an extension of your main domain. When you have it set up that way and build content the backlinks received for the content can help build the domain authority. I personally prefer to setup blogs as /blog and would recommend that method although I have also seen people successfully have subdomain blog setups as well.
