WordPress is very popular amongst self hosted blogs. That means if you will put your blog on a shared website hosting account with your own domain then WordPress is the blogging software chosen by many bloggers. Everything will be under your control.You can also use the WordPress.com service and create your blog website using their online tools and have the core same features as their self hosted blogging software which makes it easier change later on without learning a new system. Blogger is a good platform if you are never going to be hosting the blog software on your own server and provides a lot of useful tools to change the appearance of your site and being owned by google could actually be easier to be find in that search engine.
They are both good blogging platforms in my opinion so it comes down to how you want to manage your website and what plans you have to expand later on. If you want to run your website using your own web hosting account and will need the ability to add new features to your site over time then go for WordPress if not then consider Blogger..