For starters, we should dispel a myth. It is often alleged that Google has ownership of your content (copyright) when you use their blogging service. But this is just not the case. While Google controls their own intellectual rights, your website content is owned by the entitled party or writer. They post this quite plainly within their TOS conditions. http://www.blogger.com/terms.g
If your content does not remain within their terms of service, then Google has the right to close down or limit your account. Wordpress allows you to host your own blog on your hosting account. While you may have more liberty concerning your content, you must still adhere to the guidelines or Terms of Service (TOS) set forth by your hosting company (unless, of course, you own your server).
Installation simplicity: Blogger tends to be simpler to configure. If your website hosting service doesn’t offer Fantastico, the installation of Wordpress may be baffling for those unfamiliar with the server control mechanisms and FTP.
Google is the winner when it comes to customization. It’s easier to edit template layouts, styles, and colors with Blogger than Wordpress. With Wordpress, in order to make changes to a template that does not quite suit you as is, you will have to learn PHP and HTML.
Each platform offers dozens of templates; and private individuals have created even more template formats, with the numbers on the rise still. Most third-party templates are free, but they will accept donations. Don’t worry, they are polite about asking for contributions and any that I’ve seen do not spam you or require you to register — though they may request that you retain a very small and unobtrusive link to their website to help them out.
Other widely-used blog software includes Xanga, Drupal (major learning curve), Joomla, and several more.
You can get blog hosting for free at sites like wordpress.com, Blogger, MySpace, TypePad, and so on.
The bottom line is that it really depends on your technical know-how and how much control you want to have over your site. Select Wordpress if you can find a suitable “canned” template, or if you know HTML and/ or PHP or are willing to try to learn PHP. If your goal is to instantly write on your blog, and you don’t have a lot of money, then select Google.