Have you ever seen a motorcycle with a sidecar? By attaching a little car to the side of a motorcycle, you get the benefits of the motorcycle's size and open air travel and the benefits of a car's long distance comfort. Many site owners choose to do something similar by running Joomla and WordPress simultaneously. They want Joomla's flexibility and power in addition to WordPress's wonderful blogging capability. However, running these applications in tandem introduces several issues and, for a number of reasons, I recommend against using both systems together.
The benefit of using WP and Joomla together is an increase in power, by getting the best aspects of both applications. However there are some serious drawbacks:
If you're considering running both applications side-by-side, you have to ask yourself whether the benefits outweigh the costs. The question is: Can you afford to run both systems in tandem? And could that money be better directed somewhere else?
Though I believe that WordPress provides the best blogging solution, Joomla also has several excellent blogging options that work just as well for 98% of cases. For people who are primarily running blogs or similar content delivery focused solutions, I think WP is a great way to go. However, if the blog is just a component of the site's goals, I recommend taking advantage of Joomla's extensibility and fully utilizing its capabilities by using a solution like Easy Blog or a CCK.
If you find yourself in the situation of building a site with both, ask your developer about using Joomla or WP exclusively. If you're already running both Joomla and Wordpress and you're running into the above issues, perhaps it's time to look into transferring your content to one system.