Drupal is definitely a better choice for a full fledged CMS, and has a pretty great developer community behind it. Wordpress is an awesome platform, but it's not exactly meant for full websites; more of a news feed/blog with a few static pages.
I am personally a big fan of CMS Made Simple (CMSMS) I've used it on several projects and it's just really straight forward to develop, and my end users have all had a really easy time picking it up and editing their content.
I'm a huge fan of CMS Made Simple because it's easy on the developer and the user. Templates are easy to understand and create, with "blocks" for content designated as {content block='left_colum'} for example. The user gets a pretty straightforward interface to edit pages with a TinyMCE WYSIWYG editor.
I've developed maybe 40 or 50 sites on this platform and the only time I used something different was to specifically to create a blog. In that case I went full wordpress, or cmsms for the site and wp for just the blog though in that case you need to build the theme in both cmsms and wordpress.
Just my two cents, but it's worked for me. Let me know if you have any questions.
If the client doesn't want Wordpress, Drupal may be the second option. There is also a CMS called CMS Made Simple: http://www.cmsmadesimple.org/
We used this CMS for a 2000+ page University website and it was pretty good with the custom templates, useful plugins etc.
Personally, I like using CMS Made Simple, but it's fairly involved in terms of setup/coding. Has a lot of nice features, but if you aren't at least proficient with PHP it might be a struggle.
A friend recommended Cushy CMS. While I have never used it, the intro makes it look like it's super simple to setup/operate.