I have used both.
As a beginner, who is more focused on starting up his/her writing skill, Blogger gives a nice push to start with. It would introduce into the basics of blogging and you can try your hands on, experimenting with the features that it provides. If your blog is not much in a requirement for a full-fledged Menu system and other features like Forum and Discussion, Blogger is definitely good to start with and carry on for days till you don't change your mind. As it is Free, you don't feel the pinch if your Blog doesn't click, or you lose interest in between.
But if you are serious about your stuff, and looking for a platform, where the Menu has a lot of contribution to your site, then Wordpress would be the one, you should opt for.
There you can customise the entire scenario, go on add plug-ins as per your wish and take full control of your site with as many features you want.
But a little bit of technical knowledge would be required to opt for Wordpress if you are doing it alll by yourself, whereas any naive can start their blog with Blogger in no time. One more advantage of Blogger is the sign in process, where you simply need to visit the blogger page if you are already signed in with your Gmail account. As we all are generally logged in our Gmail account, it takes you to the Blogger skipping the sign-in page.
The other thing is coordinating and synchronising with the sharing pages of Social Media, which is easier in Blogger than that of Wordpress, and to get traffic to your Blogger page you need no extra effort as such, whereas Wordpress would not make these things that easy.
So depending on your current and long-term plans, you can choose among these two.