There's no doubt that Wordpress is easier to learn, quicker to deploy and more popular for those reasons alone, but Joomla is undoubtably more powerful as a solution and if your willing to accept that its more complex to setup and maintian then the benefits can far outweight this.
Joomla, at its heart allows for complete customisation of the experience whether that by via CSS, templates, styles, or through modules, embedded plugins and even embedded PHP and JS directly into the render. When your looking for a CMS solution that can take your business to any destination then Joomla is the one to select.
There are many examples online showcasing the flexability of Joomla, but we prefer to just say, whatever you want, we can do. A good example of this would be a recent customer portal entirely in Joomla, with data extracted from a SQL Server database over the Secure WAN and presented to customers via interactive tables, graphs and downloadable content.
So, if you have a CMS project and want to advice, just drop us a message. If you've already got a site in Wordpress or Drupal and are looking to go a step further, again just drop us a message.