If you do not need the stuff that Joomla provides out of the box - and that is a considerable amount - wordpress could work well for you. Most everything that can be done with Joomla can be done with wordpress (but certainly not here at wordpress.COM).
I have a pretty slick local install of Joomla going on my computer and it will most likely at some point replace my wordpress blog installation. With Joomla, I like the fact that I can, if I wish, have each page of the site equipped with different sidebars and such. I like the fact that I have more options on where to place the different extensions and such. I can do that with wordpress also, but it typically means "hacking" a template and the CSS into submission and I'm not that well versed in PHP script.
Vikasjnu is right though, Joomla has a steep learning curve and for standard, or even slightly non-standard blogs, it is overkill.