This question is like asking which is better, a hammer or a screwdriver? The answer depends on
whether you're trying to drive a nail or twist a screw.
Joomla and WordPress are both robust content management systems (CMS), but each was designed for a different purpose. Like a hammer and a screwdriver, they're different tools.
Vivid Vision specializes in custom built Joomla packages and so Vivid contracts with businesses whose needs are best suited for Joomla and not WordPress. For example, one of Vivid's current clients, International College of Ministry, has over 1,300 pages, in dozens of categories, in their live online school. Another current client, Certa Books, has over 600 pages in their custom ecommerce Joomla site. Both clients need Joomla's ability to manage a large volume of content, manage ecommerce functions, manage event registrations, manage user access, and staff administration and training. Joomla is a perfect fit for these clients. However, a client that needs a 10 to 20 page static website would not be a good fit. For that kind of client, WordPress is a better choice.
So the better question is, "Which is the best CMS for my needs?" Vivid's blog article linked below may help you find the answer.
For a detailed comparison of WordPress and Joomla's strengths and weaknesses, check out Vivid's blog article Joomla vs. Wordpress Which is the Right CMS for You?