Both are batter option. Google count a sub domain as another website so If you are selecting url like blog.site.com is called individual website it self Or If selecting url like site.com/blog becomes a microsite of that particular domain. Both way are good, no harm on your seo on the site and blog, blog can rank if you submitting healthy content and good back links.
Both are good but we can build good inter linking within site.com/blog that's why I would like to go with site.com/blog. Just go with it.