The Drupal (news, site) vs Joomla (news, site) vs WordPress (news, site) debate is one of those theological disputes, where each of the sides asserts their rightness with emotional, rather than rational arguments. Kind of similar to the dispute about open source vs proprietary code.
However, the difference is that all the three platforms are open source and they are also frequently named the three most popular ones. Well, maybe the discussion about who rules the (Web CMS) world isn't as heated as the discussion about open source vs proprietary code and there are less casualties but still this discussion is pretty heated.
The Verdict of Popularity: Drupal 40%, Joomla 6.2%
The answer to the question which Web CMS is the go-to project for high-end projects depends on whom you ask. It also depends on what a high-end site means – unique design, stability, security, millions of pages and transactions, etc. For a small site or blog, WordPress really rocks and is a very popular choice, while for large and/or high-end sites you might encounter way too many issues to be happy with it.
Actually for a blog, WordPress is the undisputed leader with about 90% of all blogs running some version of WordPress (source: Built With); for a CMS, Drupal rules with 40% (source: Built With). Joomla comes nowhere close with the modest 6.2%.
Of course, these figures don't mean that Joomla is just a minor player nobody takes into account because Joomla is still a popular choice and it has its advantages over Drupal. For instance, Joomla is much easier to get familiar with by non-techies, which isn't a minor issue when the system will be used by a client who hasn't heard about HTML and PHP.
Drupal Is for Techies
On the contrary, Drupal is for techies. Drupal has many advanced features Joomla and WordPress lack, such as views, taxonomy, or semantic features to name a few but it is more complicated and does require sound technical expertise. Probably this explains why Drupal projects have the largest budgets.
For instance, a recent report by DoNanza, suggests that “Most CMS Sites Use Wordpress While the Largest Budgets Go to Drupal Developers”. DoNanza is a work-at-home search engine and they do have access to lots of statistical data. To some extent, it is strange that they compare demand for WordPress and Drupal projects/developers and exclude Joomla from the picture because the site itself has a bias towards Joomla - there is a special category for Joomla projects on DoNanza, while the other Web CMS are just part of the Web Design category.
In any case, the findings in the survey give an answer to the question about the popularity of Drupal and Joomla for high-end projects. The fact that Drupal projects draw more dollars probably means that these projects are larger and more complex, i.e. the sites are high-end sites.
Drupal definitely leads in this segment and many people prefer it as the platform for larger and more expensive sites. Of course, this doesn't mean that you do should do the same but when the trend is for Drupal to lead in the high-end segment, there must be a reason for this.