I personally use Blogger. I like the convenience of Blogger being part of Google. Makes it easier to have only one account for blogging, youtube, email, google analytics etc. But that depends on whether you already have a Google account of course.
Here is the main difference in my opinion: Blogger allows you to customize the templates for free. WordPress does as well, EXCEPT you have to pay. Blogger allows you to insert third-party visitor trackers to count the number of visitors etc. (not to re-mention the ease of access of Google analytics once you have your Google account for blogger) For WP you have to use the built-in one, which is less detailed. (only 2-day stats, and beyond that, just weekly and monthly graphs)
If you already have a blog and want to transfer it to a new platform, Blogger only imports other blogspots, whereas WordPress is compatible with most major blogging platforms.
You can store 1G of pictures on Blogger, 3 on WP. WP has a built-in option to include a contact form. You have to use a third-party in Blogger.
I prefer Blogger overall, mostly for the higher flexibility. If you want to really customize your blog, you can do it more easily in Blogger than WordPress (again, unless you pay). However I’d say WordPress is perhaps simpler to use when you want a quick solution to start blogging fast.