What are the advantages of using an MVC framework over e.g. Drupal to build a large website?

I would advise you strongly against WordPress, it is wonderful for sites with some static pages and one blog/news section, but I made a bilingual product website based on WP 2.2 and it was a major PITA with lots of hacking and writing database-reaching code into the template to make it possible.

Now I have been developing in Drupal and it is really better for larger projects (although it takes more time to set up a simple blog compared to WP) - it has wonderful modular architecture that allowed me to solve any request/problem so far by writing a module instead of hacking the core.

As for MVC/Drupal: have look what Drupal does, if you can get your result by modifying Drupal, then it is great and will save you a *lot* of time by not having to code the usual stuff (user registration, input sanitization, robust form handling and validation, theming infrastructure, storage abstraction, web services abstraction layer (Services module) and so on...).

Against Drupal: inherently slow, due to modular (I'm rendering a list of items, let's call all modules that implement theme_list to find out if they want to modify it) architecture, so if you are making next twitter, get a fast MVC framework instead. And caching of content for registered users still needs lot of work to be effective (a tagged cache should be in core), so sites when users are usually logged in can be slow.

It's difficult to compare a CMS (e.g., Drupal, WordPress) with an MVC framework because they are in different categories.

To specifically answer your question about the advantage of an MVC framework over a CMS, the advantage of an MVC framework is simply that it allows you to design the exact web app you need from the ground up.

As for your particular situation:

Using an existing CMS such as WordPress or Drupal would be an excellent idea if they fit your needs. It avoids reinventing the wheel, saves you time, and CMSs can be quite user-friendly (to varying degrees). If you plan to delegate the task of content updates to a non-technical user, then it might be prudent to choose a novice-friendly CMS rather than spinning your own with an MVC framework, possibly resulting in an app that requires more technical expertise to maintain.

If, however, you envision that the website will require a lot of custom business logic that would be difficult to implement within the constraints of a CMS, then you might need to use an MVC framework.