If this site involves e-commerce, I would recommend Joomla, since there's a popular e-commerce plugin for it called VirtueMart. Joomla has good community support, many plugins, and its features make it very scalable and customizable. Joomla also has good user management. However, using Joomla can be difficult at first, as its content organization is rather complex.
If the site would consist of basic blog-like webpages, then WordPress is the way to go. WordPress is a very simple blogging CMS with a huge user community. It's very easy to use, has many plugins for it, and the newest version of WordPress even has auto-updating features. WordPress isn't as good as Joomla when it comes to user management, though. For example, Joomla can specify exactly what content users and user groups have access to. WordPress has basic user groups, but additional customization and plugins would be required to have that functionality.
OpenSourceCMS contains demos for both Joomla and WordPress.
In my past web development experience, I've used both Joomla and WordPress for my clients. Joomla typically requires having a sit-down with the client to go over the basic features of how to use the software, while WordPress is easy enough for the client to figure out without any assistance. However, the WordPress sites I've worked with that require more than the standard blogging features (e.g., e-commerce, image galleries, forums) usually involve integrating WordPress with a separate software application, while Joomla more often than not has those plugins available for it. The end result is a website with several applications on it installed (e.g., WordPress, Coppermine, phpBB), each with separate logins and admin screens.
For a simple and easy website with basic features, I would suggest WordPress. For a website with specific needs (such as e-commerce) and the potential to scale, I would suggest Joomla.