Both, but it depends on the type of site that you want - If it's just for sharing pics and the like, then a blog is great, but if it's for business then you should really have some static content for users, as it's what they're generally used to seeing when browsing the net.
There's no reason you can't have a blog as an addon to a static site, but you shouldn't "just" have a blog if it's for a business
IMO