Why these two CMS's, of the thousands of content management systems available? Both CMS's share several key qualities:
Drupal has extensive functionality for allowing people to interact with one another via your website. Creating accounts; logging in to access special content - or create their own; connecting with one another - all of these are possible with a Drupal site, so if your short- or long-range plans include turning your website into a social hub for your visitors, Drupal is a better choice.
In Drupal, if you have administrative privileges, and you are logged in, you can edit your content simply by navigating to the page you want to update, and clicking an unobtrusive "Edit" tab. Many people find this a particularly intuitive approach to site editing. (Not only that, but Drupal is so profoundly customizable that if you want to, you can create custom themes for different areas of your site - so your back-end could look totally different from your front-end, should you feel so inspired.)
Drupal has some very clever ways of cross-categorizing content, so if you have the kind of website where you want content to appear in multiple places based on various categories you assign to it, Drupal may be just right for you. And it's often the better choice for managing complex kinds of content, where a simple 2-field "Title" and "Body" editing screen won't suffice.
The underlying architecture of Drupal is quite flexible, and the CMS can be adapted for a wide variety of purposes. Drupal is like a Swiss Army knife or a food processor: it is many tools in one, and you can choose to use it for one task or several. WordPress is much more specific in its function: it does a handful of things and does them very well, but it isn't the right tool for every job. (On the other hand, if you need a simple site, Drupal may be overkill, and you could spend a lot of time turning off the features you don't want.)
Drupal's out-of-the-box configuration is somewhat limiting, and most people prefer to customize it pretty heavily. This requires not only a solid understanding of HTML and CSS, but also of PHP and of Drupal's underlying architecture, which has a fairly steep learning curve. As a result, Drupal sites tend to cost more to set up, though the initial investment is well worth it if you plan to extend your site's functionality to take advantage of Drupal's flexibility.
I personally find Drupal's blogging capabilities somewhat limited - for example, creating blog category lists, tag clouds and date-based archives is rather onerous in Drupal, whereas in WordPress they take a matter of minutes to set up. WordPress was first developed as blogging software, and it shows: its blogging features are well thought-through and have been polished by years of improvements.
WordPress's "Media Library" feature allows you to browse through all the files you've uploaded to your site - images, PDFs, multimedia files, whatever they might be - in a clean, attractive & easy-to-use interface. It makes managing your files and inserting them into your blog posts and site pages a much easier task.
Because of WordPress's blogging focus, the developers had to pay close attention to managing spam. (Blogs attract a lot of spam via comments and pingbacks.) WordPress comes bundled with spam-filtering software that does a remarkably good job - and moreover, its comment-management features are well thought-out and simple to use.
WordPress is famous for its 5-minute install, and it really does live up to its name. Although that doesn't mean you'll have a fully-functioning website in 5 minutes, it works well "out of the box" for most simple sites & blogs. As a result it is often less costly then Drupal to set up.
Both Drupal and WordPress have a great deal of flexibility with regard to visual design - you can make a site built in either CMS look beautiful via either free templates or by applying your own custom design. However, theming a Drupal site is a much bigger task than theming a WordPress site, unless you are simply going to download a free theme and slap it on your site. If you want to be able to tweak design details, in our experience, that's a much faster job in WordPress.
If you aren't planning to use WordPress's blogging features, navigating through the CMS can be a little confusing, because blog posts are the primary focus in the menus, and page editing is less prominent. In this sense, its focus on blogging can be a weakness as well as a strength.
WordPress keeps your site's back-end (that's the area where you create & edit content) totally separate from the front-end (the part your visitors see). Some people (like yours truly) prefer this approach, where content is more or less divorced from presentation, whereas others prefer Drupal's integrated editing options. In my experience, this is a highly subjective preference, and it's worth trying both to see which feels better to you.