NOTE: Rather than posting an exhaustive comparison of the two, this will be the first post in a series looking at what sets them apart and why you would be better off with either in particular situations.

Both Joomla and Wordpress are industry-leading Open Source publishing platforms that make it simple for people with no knowledge of HTML to create blogs and publish pages to their website easily and quickly.

However, they are each built for different core audiences - Wordpress is essentially a blogging tool; extending its feature set beyond blogging requires the use of FTP and custom code - so it is best suited for individuals and small organizations who have an on-going relationship with a web developer who can provide upgrade and feature developments for them.  This isn't to say that it can't be used to create highly usable websites with creative aesthetics; but just that doing this takes more elbow grease than with, say, Joomla.

Out-of-the-box, Joomla allows users to create dynamic websites which incorporate a powerful menu system that allows dynamic displays of content - not only for blogs but other lists or tables of content items, with just a few clicks of a button.  Innately, Joomla websites can be grown by uploading sub-programs (eg an e-commerce package or discussion forum) directly through the admin interface in a browser- no need for ftp or dealing with any code whatsoever; Joomla offers more powerful yet easier scalability than Wordpress.

Another major feature that sets the two apart is the ability to edit posts from the front-end; managing a Joomla site can be much faster and visually understandable as only admins need to see/use a dashboard/admin side of the site - anyone with content submission/editing permissions can simply log into the front end of a site, be shown the edit button [or submit new content] and make changes live to the site.