I have used both extensively.
Advantage of each:
Blogger
- It's owned by Google so it automatically connects with Google+ and the entire Ecosystem.
- Easy to use and set up. Out of Box Ready
Wordpress
- Awesome Plugins, and limitless design and customization
- Great for SEO
- More Complicated to use and required a bit more hands on approach.
Personally, I strongly prefer Wordpress which powers 23% of the internet!