Drupal is definitely lively. I could be wrong, but I believe its growth rate is higher than Joomla, though it may not have as many installs yet (and of course neither one is remotely close to WP). It runs big sites - whitehouse.gov, NASA, The Onion. So it's capable and very actively developed.
For what it's worth, Wikipedia says Drupal runs 1% of all websites in the world now. In fact, that article is actually a great overview
One thing I like about Drupal is all the security warnings. What?!?!? you say? Yes, unlike Wordpress or Joomla, any Drupal module that is stored on the Drupal site (99%) are treated similarly to the core distribution. Meaning, if a security exploit is found in a module, you will get emails and messages on your site (also, unlike WP, Drupal discerns between bug fix notices and security notices - if my site is working, I ignore the former).
Drupal has just released Drupal 7, which is quite nice from first looks, though I have yet to create a site with it. Of course, a lot of modules have not been updated for D7 yet. So that's a major consideration. I would say, if at all possible, build in 7. Drupal's current philosophy is a release every few years, with security support for current and former. So D6 will have support for a while, but if you build it in D7, you're likely to have at least 5 years before EOL.
As for why your client is stuck on Drupal, it's no doubt because someone convinced him that it was the best and he doesn't know any better to ask "Best for what
My rule of thumb for Drupal is this: If Drupal does what you want out of the box, you probably don't want Drupal.
Where Drupal shines is as a framework that can be tweaked and do things undreamt of in Wordpress and Joomla. Where it falls down is in complexity, server load (much higher than WP) and sometimes the difficulty of getting it to do simple things.
I think that characterization is changing. Drupal has been working on ease of use and streamlining. Joomla has been trying to copy some of Drupal's in-built power (Views, Panel and CCK) but still isn't close.
So if you know WP and Joomla and know this project and his future vision can be done with them, I would try to ask him why Drupal and see if he'll budge.
If not, pad your bid for the pain of getting your head around Drupal. Once you do, though, it's like a drug. It's hard to do without it.