The first question to address is, what are the differences between the two. Many different people will offer many different answers to this question, but the best description I've been able to put together is as follow:
A blog organizes information by time whereas an article based website organizes information by content into information structures (example: categories)
What this means is that although we perceive blogs and article sites to be quite different, the content contained therein in relatively interchangeable. I say relatively because blogs are often much less formal than a comparative article based website. The informal nature of blogs is simply a socially influenced norm.
Blogs were great for informal writing when they began because none of the information needed to be organized logically. All of the content organization was handled based on the date of creation. Once people saw examples of informal, personal blogs, they caught on like wildfire and have resulted in what we recognize as blogs today. But if you look at some of the more "professional" blogs, you'll find content that's written in such a manner that it could easily be presented as an article and be part of an article based website.
Similarly, on the other side of the coin, there are websites that appear to be article based, but could easily be converted to a blog format. Any article based website that has ongoing content development and/or articles released on a regular schedule can take on the blog format and still make a lot of sense.