Joomla is an advanced CMS system whereas WordPress is yet another blogging platform.
Joomla needs you to make some customizations in order to get a higher ranking by the search engines whereas WordPress is very SEO friendly by default.
WordPress is mainly used for displaying content, for updating the website and also for frequent additions. The number and complexity of the plug-ins offered by WordPress is growing each day, but they are yet as complex as the plugins and modules offered by Joomla. The Joomla CMS system of Joomla is very flexible and programmers can do lots of things from creating a small website to adding more extensive features to it.
Joomla administration area has features like order management, e-commerce, document management and inquiry management. All these features makes it a complicated software to use but the end result is worth all the hard work an user undertakes for building a website. The administration area of WordPress is very simple and intuitive but can be mainly used for publishing.
Joomla can be integrated with 3rd party software very easily because of its API which can be used by web designers or webmasters for integration purposes.
As a conclusion, both Joomla and WordPress offer great advantages to their users for creating and maintaining websites. Most of the users can handle the content management system of Joomla after the website is in use, but the initial creation and all the tweaks and customizations involved still need professional web design & web development. The best thing would be to use these two systems together and blend their best features.