I have used both DNN and Drupal to build fairly large, content-based sites. My focus is more on the production side... UI/themeing, module configuration, etc. I'm sold on Drupal, but there may be other choices that meet your needs just as well. I just happened to work with both systems in recent months.
Drupal's core taxonomy module gives you the benefit of creating a relationship between different kinds of content. If you have "article" and "video" content types, you can easily display data from both types based on the shared taxonomy terms. This is huge and something DNN lacks.
Drupal's hook system is also a big benefit when building your own modules or creating "sub-modules" to alter or add to the default functionality of an existing module. This allows you to customize functionality or take advantage of another module's functionality as your application runs. If you purchase a module for DNN, you will have to alter the module if it doesn't meet your needs. Once you do this, you will need to update it each time there's a new release that you would like to take advantage of. DNN modules seem to be more stand-alone solutions. For example, if a DNN module has a rating system, it's only a part of that solution. With Drupal, I can use the "5 Star" rating module in my forums, my blogs, my articles, my videos, etc. There's central configuration for it and I only theme it once.
The themeing layer in Drupal also gives you a large amount of flexibility in that process. My frustration with themeing DNN sites was that I was stuck working with the markup the developer used, with no option for altering the output without hacking the module. With theme hooks and function overrides, I can change the output from those modules to meet my needs (not completely sometimes, but enough), without touching the module code itself.
The biggest problem I had with DNN modules, including some of the most popular, was just a lack of documentation or discussions available for how to achieve your goal. While Drupal's forums can be hard to navigate and you might not always find the answer you are looking for, there are many outlets for gathering information. Honestly, using DNN made me appreciate the community approach of Drupal more.
I was left feeling that DNN would be fine for building sites with more basic needs. But for that, I would still choose something like WordPress or Joomla, considering they have much larger user bases and, in my opinion, are more sophisticated.