Let's put this rumor to rest: It's rumored that Google retains rights (copyright) to your content that you blog with them.
This is false.
You have the rights to your content, but Google keeps the rights for their intellectual property.
Their terms of service (TOS) explains this in detail.
If your content does not remain within their terms of service, then Google has the right to close down or limit your account.
Both allow you to host your own blog on another server.
While you may have more liberty concerning your content, you must still adhere to the guidelines or Terms of Service 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.
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.
Quite a few templates are included with each platform, and a vast number of templates have been developed by third-parties -- a number that continues to grow by leaps and bounds.
Other widely-used blog software types include Xanga, Drupal (major learning curve), Joomla, and much more.
You can get blog hosting for no cost 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.