I think your question is a little ambiguous. Are you asking about Blogger.com versus Wordpress.com? Or are you asking whether you are better off with a stand alone blog running Wordpress as a content management system?
If your question is Blogger.com vs. Wordpress.com then my answer without a doubt is Blogger.com. I know that opinion is contrary to what others have written. But, here is why.
You tend to see a lot more www.whatever.blogspot.com
websites listed in the search results than you see from whateveryournameis.wordpress.com.
In fact, I hardly ever see a blog hosted on Wordpress.com actually ranking in the results at all. So I would take Blogger.com anyday. There are other reasons too that would be far to complicated to explain in this little thread comment.
On the otherhand, if you are aksing if you should use Blogger or a self hosted blog running Wordpress content management system, then my vote is 100% for the stand alone Wordpress blog.
Hope that all makes sense.