One of the new features of Blogger is that you can host the application on your domain. (I noticed they offer using your Google Account login on the new platform, too. That's nice). WordPress has offered to host your blog, customizing your theme, adding plugins, etc. for quite a while now. I believe it's one of the key reasons why I chose WordPress… I wanted to own my domain.
The problem with starting your blog and running it on one of the many platforms, vox, typepad, blogger, or wordpress, is that they own your traffic, not you. You are reliant upon their servers, their platform changes, their downtime, everything! The only thing you ‘own' is your voice.
That's not a big issue if you just want to keep a journal out there. But changing your mind down the road and deciding you want to be serious about blogging, perhaps get some advertising, etc., and guess what? You're stuck… all the major search engines now have your voice (content) indexed at someone else's website. That means they own the traffic, not you.
And what happens if they go belly up? What if their server performance or software gets so inexplicably terrible that you need to leave them. Fortunately, you can take your posts with but, unfortunately, you can not take your search engine indexing. That can set you behind for weeks and months as you wait on everyone to index your site and update all of their references to your site. This weekend, I moved my site to a different account, and all of my links and search results continue to work as they did before. I would also recommend utilizing a permanent link structure so that if you move to a different platform, you can maintain your link structure.
My advice to new bloggers?
Own your blog domain! Don't even let your ‘techy' register it for you. You need to own it, you need to renew it, you need to keep track of it. Owning a domain is like owning your street address, would you put that real estate in someone else's name? Why would you do it with your business or your blog?
My advice to blogging platforms?
Offer name server services. This would allow me to register a domain name with my favorite registrar, but point my name server to your site. If I decide to move my blog or site to a different host, I could simply move my site and update my name server. This could be a ‘pay per use' model as well. I would avoid domain name registration services since they can be a pain in the butt and you'd have to add all sorts of support and integration to your site. But having a domain name server that points http://mydomain.com to http://mydomain.theirdomain.com is quite simple.