Joomla is a wonderful application with many different groups of people using it for many different reasons. I've been working with it for over five years, however in that time I've also worked with several other popular solutions. I've chosen it as my business focus and my primary development platform because I believe it's technical advantages are superior for most development scenarios. If I were to sit down with an organization choosing a web platform, here is the technical case I would make for it.
It's written in PHP. It's been popular for many technical folks to denigrate PHP(though rarely programmers who've actually developed with it), however PHP is a strong web development solution that powers most of the web's applications, including bemoth's like Facebook. It's a language with an abundance of solutions and developers and is very well documented. All of this combines to lowering the total cost of the solution and making it much easier to find good help.
It's Open Source. The benefit of using open source is that it's continually audited for security holes and offers decentralized solutions- there is no vendor lock in and you don't have to wait on one organization to get help or seek answers.
It's Built On A True Modern Framework. The same two above points could be said about Joomla's popular CMS alternatives: Drupal and Wordpress. However neither Drupal nor Wordpress can claim to being fully object oriented or built on the common MVC architectural standard. This is important because Joomla offers the same kind of development environment as web frameworks while also still offering the benefits of using a CMS. Most web applications have crossover: content, menus, widgets, ACLs, user management, caching, and interfaces. Joomla gives developers the ability to quickly write applications like they would with a web framework, but also pre-built access to these already well coded common needs. You get the advantages of the bespoke while also accessing the advantages of the pre-built.
It's Extensible. In addition to offering a modern code base to do custom development with, many non-core custom needs are already met in the form of a vast library of plugins, modules, and components in the Joomla extension directory. This further limits needed development time and enables you to make cheap leaps in functionality. Agility and speed are key to online success and developing in Joomla offers both.
It's Popular. Though the web isn't a popularity contest, popularity matters. The more popular a solution is, the easier it is to find resources to support and extend it. Joomla is very popular, routinely winning awards for best open source CMS.
These are just a few reasons why Joomla makes a superior technical solution. If you're a developer, I encourage you to download a copy and pop the hood— you'll be impressed. If you're planning for a business or organization, give it some serious consideration: the combination I've presented here offers long term value that is unique to Joomla.