We personally believe both Drupal and Joomla are pretty equal in what they can do. They both are robust systems that are ever evolving and have tons of add on modules and extensions to further enhance their capabilities. Further more, we have the ability to manipulate the source code to our hearts' content. With that in mind, they could be virtually the same. You can always adjust the code to add to whatever the CMS lacks.

Does size matter?

Right out of the box, when you are installing the CMS of your choice, you will see an immediate difference between Drupal and Joomla. Drupal is about ten times "smaller" than Joomla. Drupal has about 463 files in it's initial installation and Joomla has about 4150 files in its initial installation. To us the less bulky the software is the better, so Drupal wins in this instance. We usually side with Drupal for this reason. Drupal seems less bulky and somehow the code seems cleaner, thus, faster loading time, more accessible, and more search engine friendly.
Administration Usability

It is our clients who ultimately have a hand in the decision of which CMS to use. We first ask what are their goals for the website. One of the biggest deciding factors is if they want to manage the site by themselves or do they want us to manage the updates and content. Out of the box, I find that Joomla has a somewhat more user friendly administration panel. The default administration theme has icons that represent the different areas like Article Manager, Menu Manager, etc. Joomla also has a built in WYSIWYG (What You See Is What You Get) editor which is very important for most clients who don't have any HTML or coding experience. Joomla also has a more intuitive media manager for pictures and other media. Drupal has a text based administration area and may take some getting used to. And if you want a WYSIWYG editor, you'll have to install a module. Really though, we have clients who manage their own site and we are using Drupal for them and they don't have any problems updating the content. Both of the CMSs, have a learning curve and if the client only has the one goal of adding an article or a blog page every now and then, they can learn the process with either Drupal or Joomla and be fine. If administration usability is of utmost importance for the client, then we think Joomla may win with its graphical interface.
Forum Functionality

If the client wants a forum, we probably would go with Drupal, because it has a built in forum module. With Joomla, you would have to install an extension. Kunena community builder is a good forum extension for Joomla.
E-commerce and Banner Ads

For e-commerce, we have the most experience with Drupal and Ubercart. Ubercart is a great e-commerce module for Drupal. Together, they are a wonderful combination. Of course, Joomla has e-commerce extensions too, but our experience is limited with them, so we go with our experience on this one. If the client wants a way to sell banner ad space, Joomla has a built in banner ad manager. It is a great built in function that gives statistics on how many times the banner ad was shown and how many times it was clicked. The banner module can take images, video, and flash (I'm currently developing a marketing tool theory using this banner ad module, article coming soon.) Drupal doesn't have a banner module out of the box, but there are modules you can install.
Blogs and Organization

Both CMSs have "blog" functionality. Drupal spells it out and has a blog module that is very effective. Joomla goes about it in a somewhat different way, but its method actually is the foundation for a more organized system. Joomla essentially forces you to organize your articles into Sections and Categories, therefore, essentially forcing you to be more organized - which is a good thing. With the creation of menus, one can point to one article or a whole section of articles or a whole category of articles. The latter two, can be used to make "blog" sections/categories of your website. For example, you create a menu item "Electronics" that points to a section you made "Electronics". And whenever you create an article about electronics, you put it in the "Electronics" section. It will be appended to the growing list of "Electronics" articles, creating a "blog" about electronics. One could essentially make their whole entire site (each page) section based that is constantly changing (if they had the wherewithal to keep adding content.) Joomla kind of wins in this area because of the "forced" organization. It makes it easier to manage and organize your content.
Modules and Extensions

For both CMSs, there are modules and extensions that do just about anything you can imagine. When one is looking around for extensions and modules for either Joomla or Drupal, they will notice also that the Joomla library of extensions if more graphical and more usable. Drupal's module library is mostly text based. While these details don't say anything about the two system's effectiveness, it may persuade people to believe Joomla is better, because it's like "ooh shiny!" "Joomla is cooler because it looks better!" But really, the way your site looks or anyone else's site is mostly based on the imagination and skill of the designer, not really the back end code, and both Joomla and Drupal can be manipulated to look like whatever you want.
Our Opinion

We like them both! We use them both! So yeah, what's your opinion?

~ Josh