I have used both in various projects. I found with Joomla, there was always a number of components and mods out there to help along, but they were never quite right. If you wanted anything that actually worked, most of the time, you had to get a purchased version.
Then when it came down to customization. Yikes. I retained a programmer for over a year making updates and changes to one particular site. He had to mangle that code in so many ways, I now have no way to really migrate to updates without breaking everything.
The coding of joomla is WAY WAY more complex than wordpress.
I disagree that wordpress is just a blogging platform. All it takes is a plugin or two and it's just as CMS enabled as joomla can be.
Joomla over complicates things that could be made simplier. Wordpress on the other hand has gone to great lengths to make an admin interface that is one of the most intelligent in the industry. While joomla always (and I mean always) leaves clients with deep in headlights syndrome the moment they login.
Many of the major joomla components are slow to update. Development of new features are slow, and joomla itself is slow to update. Wordpress on the other hand as you can see is constantly making strides in improvements.
As for security, I have had more Joomla sites broken into/hacked than Wordpress.
After all my experiences, when it comes to new projects, I don't even debate anymore. I go with Wordpress right away. I know I will save a ton of time over Joomla or any other CMS in setup time, frustrations, and overall costs.
Good luck with your decision.