Let’s start with Joomla first.

Joomla is designed to work well in shared hosting packages. The look of Joomla’s installer looks much the same like the installers used for common desktop software, as well as the administrative interface that content editors use. There are a small number of entry barriers when using Joomla and it should take little time for website developers to get familiar with the system. If you need extensions to cater for your website and that are not available at extensions.joomla.org, it would not be too expensive for you to get a programmer to design one for you as Joomla is written in PHP, which is a widely recognized script language specifically designed for website development.

Joomla can be a fantastic choice to build a professional website with lots of pages, content types such as events and news items and strong navigation. Unfortunately, it has limited functionality when it comes to dynamic content structures. One example is the website navigation is only allowed no more than two levels of hierarchy, and you can only link one page to another based on free-form page tags, rather than more accurate metadata and rules.
I have taken ideas from a few websites to help list the pros and cons of Joomla.

Pros of Joomla

• Easy deployment
• Large community of developers (more than Drupal) for helping with setup and development
• Multi-lingual. Translation and language support in modules. Works most of the time.
• More intuitive administration user interface
• Editing content is simple
• Lots of polished modules for things like calendars, polls, etc.
• Easy addition of modules. Good modules that works as advertised and have many options, supported by the authors, commercial or not. Lots and lots of modules, professional ones too. Modules for most everything.
• Versioning is available
• Most of the most popular modules and Joomla itself, is bug-free. Ok, there might be a few work-arounds needed, but you can mostly work around them, or maybe you just misunderstood something.
• There is SEF and SEO, alas not as good as Drupals, it works and you don’t need too many modules for something decent

Cons of Joomla

• 1 installation of the software gives you 1 website
• Modules cost you money
• Limited roles and permission allowances
• Categories can only go two levels deep
• Out-of-the-box blogging functionality is mediocre
• URLs are not search engine friendly (there is a purchasable module)

Ok let’s move on to Drupal. Now Drupal, like Joomla will work well in a shared hosting package. It is easy to get started like Joomla but it will not be as easy a set-up compared to Joomla but if you are technically savvy, you should not have too much trouble there.
Drupal has many great and extensive tools for content editors or developers to design websites without the hassles of going into the code and offers accessible standards-compliant pages. Its workflow makes it simple for developers that need multi-level approval processes. In addition to that, Drupal offers deeply integrated plug-ins for incorporating other specialist tools.

Pros of Drupal

• Easy deployment
• Editing tabs integrated into actual pages
• By far Drupal’s strongest feature is its category structure known as taxonomy. This is whereby Multiple levels of categories are allowed along with an easily integrated tagging system
• Modules are plentiful, free, and suitable for non-profits
• Human readable URLs which are search engine friendly
• 1 installation allows you to create and manage multiple websites (very handy when creating campaign sites)
• Highly configurable user permissions handling
• Editing content is simple as well
• Very flexible in its configuration
• Many high profile sites use Drupal (e.g.: MTV UK, BBC, the Onion, Nasa, Greenpeace UK, Kleercut )

Cons of Drupal

• Administration area is clunky, but it’s getting better with each version
• Support for the free modules can be frustrating
• Adding a visual theme to Drupal can be time consuming
• Terminology in the administration can be cryptic

So finally the decision comes down to which one will you choose? It really depends on your website. If you are looking for an easy to use content management system to manage your content, I would suggest Joomla. If it is a community building website where you require integrated and extensive tools, then go with Drupal.