Here's a bunch of pages that compare the two:
Personally I use Wordpress because I heard that it had better search engine optimization capabilities and it's very extensible with all the plugins and themes you can download. (Here I'm talking about wordpress.org, where you download the wordpress software and then upload it to a hosted space of your choosing)
These are some other people's views on Wordpress vs. Blogger:
Blogger.com vs. wordpress.com « Miles to go… Which Blog Service is the best? Wordpress vs Blogger vs LiveJournal « Tryst with Linux and other Alternatives Battle of The Blogs: Blogger vs. WordPress Blogger vs. WordPress Hosted Blog Comparison: Wordpress vs. Blogger at Awakened Voice Wordpress vs Blogger... - Technical bliss