Blogspot has more authority in Google search due to it being owned by Google.. It is very easy to use and can be changed to look as unique as you like.
Wordpress has more in the way of plug ins and themes but depending on how technical minded you are, these may be completely irrelevant!
I would suggest trying both. However, do not choose one and then change your mind after posting several times as this will eradicate any authority you have built up and therefore you will be starting over in terms of search engine optimisation (people finding your blog in search).
Hope this helps,