When I decided to create this website the first question that came up was: which CMS will I use? I built a previous version with Wordpress which is pretty much ideal for a blog-oriented website. But as it happens I built several websites with Drupal already and I currently work as a web developer using Drupal Commons to create a major new website relating to Dutch history. Noblesse oblige I felt, and therefore decided to go for Drupal. As it turned out, building a blog in Drupal was a good way to find out more about its strenghts and weaknesses in areas that also matter to the project I mentioned. 
Now before I continue I should make one thing very clear: this is not about Wordpress versus Drupal. Plenty of energy has been waisted on comparisons that often miss a basic point: they are not similar beasts. Wordpress is long past being the blog system it was and has matured into a flexible and user-friendly light weight CMS. But there are clear limits to what you can achieve with it. Drupal, by contrast, was conceived as a CMS with which people can built highly complex websites.
Which system you chose depends on what you need and there are plenty of cases where chosing Drupal to create a website makes little sense and would be overkill. Moreover, Wordpress is very popular in the digital humanities world and some useful plugins have been developed for pedagogical purposes or enhanced publication. 
So why would you want to build a blog with Drupal instead of a system like Wordpress which provides all the necessary functionality out of the box? Short answer: functionality. Slightly longer answer: when you require functionality that Wordpress cannot (easily) deliver. Or when you are not sure if your website might evolve into something more than a blog. Long answer: read this very nice piece.
To give an example: I wanted users to be able to easily export my publication list to bibliographic software and embed COinS metadata for integration with Zotero. This is difficult to accomplish with Wordpress, yet set up in a minute with the Biblio module for Drupal. I also wanted to split up the content on my tag pages in types of content (publication or blog post). Again this is easy to set up using the essential Views module in Drupal. Indeed, displaying content in myriad ways is one area where Drupal shines and its power shows.  

What about Drupal’s weaknesses as a blogging CMS?

• creating and moderating content: clearly Wordpress shines in terms of easy content moderation: I maintain and edit a Wordpress website too at work and the ease with which one can create, edit and modify posts is impressive and, crucially, wrapped in a great interface. Easy content moderation is one area where Drupal needs improvement, with the emphasis on easy because the tools are there.
• out-of-the-box functionality: all the essential tools to get a blog up and running in no time are there in Wordpress. In Drupal several modules have to be installed to achieve similar functionality.
• themes: clearly there are many more good blogging themes available for WP then for Drupal, though more and more get ported.
Again, your choice depends on your needs. For me building this website in Drupal meant I could add some useful functionality. Besides that, it was also a very helpful experiment that provided useful information for the website that I am building at my institute.  

Some useful resources: 

• Building Your Blog With Drupal 7 E-book
• Howto: Drupal for bloggers
• 20 Must have Drupal Modules when creating a Blog (for Drupal 6 but to a large extent still valid)