Most people think of Joomla! as a Content Management System
Consider the fact that Joomla! is also a Blogging Platform. Case in point: This site. All the categories are displayed in a blog layout, similar to the way Wordpress displays blog posts. But the real questions is why you'd want to blog with Joomla when Wordpress was built to be a blog platform?
Let me clear the air first:
Joomla is most widely used for small business (under $1M gross/month) and startups, but is also used for Non-profit and enterprise sites as well. While I don't know the exact number of sites that use Joomla as a blog, the way I do and this site is put together, the closest that I've seen is the JoomlaBeat Podcast site created by my friend, Pete Bui.
Category and Post Structure
Joomla lends itself very well to categorization of blog posts (or articles). In fact, Joomla makes it very easy to "Silo" content, making it extremely well organized for Search Engine Optimization. You have to take some time and consider how you'll set up your blog post categories so that you can get a good silo going over time, but again, it's easy to do.
Joomla articles can more robust than posts in other platforms. Using K2, Easy Blog or even just overriding the com_content itself can give you many more configurations and options than trying to hack up another platform that wasn't made to do advanced things out of the box.
Menus and Menu Layout
The Joomla menu is second to none. period. I prefer having full control over my URLs and site links, and since Joomla allows this, I find that there is a lot more flexibility and customisations you can make on your Joomla blog than using other platforms. This isn't to say that similar functionality couldn't be achieved on those other systems, but why hack it up when you don't need to?
I also like the fact that Menus can be used just about any way you can think of. From sidebar categories to your entire tag system, you can use menus to silo the links on your site as well... Again, very flexible.
Out of the box, Wordpress just doesn't have this, and the plugins don't handle this functionality very well either. I love being able to place entirely different modules on a menu, category and page level! I can always serve the right module content for the the page or category that the viewer is on. I mean, who wants see a gallery module when you're actually on the gallery page looking at the same pictures as in the module?
Advanced Access Control
A couple sites that I have worked on really went deep in using ACL for guest bloggers and editors. Far beyond other blogging platform's abilities. Joomla is the ideal multi-user blogging platform in this respect, and while I'm usually the only one to post on my blogs, if I do have a guest blogger, they can post directly without my interaction using the access control.
While I'm just scratching the surface of a few of the ways that Joomla can be used for (and is good for) blogging, I'm sure that you see a couple advantages of using Joomla as a blog platform. Focusing on SEO, content layout and site structure, Joomla makes blogging easy.