WordPress allows you to fully explore and customize your blog. You can use download and
install it completely for free and start using it right now. Installation process is very easy and informative, specially oriented to the beginners and amateurs. With a free-hosted solution, you don't need to install a WordPress blog. It's installed once you open a blog. But, you don't have a functions that are included into the self-hosted solution like:
Full Customization Customize your blog through third-party plug-ins and themes. Allows you to highly improve your blog functionality and productivity for sure.
SEO For Wordpress Free-hosted blogs can't change and improve the SEO functionality of your blog. Just because you can't install any third-party plug-in from their database.
Advertising Potential It's really hard to advertise (and make money) from your self-hosted blog. So, if you expect to get a full earnings potential use the self-hosted WordPress blog for sure.
Domain Name If you already have a domain name you can't use it by the default (for free) with your free-hosted powered Wodpress blog. Using self-hosted solution gives you the option to build-up your blog aroundown domain name.