.ORG blogs are pretty much wide open, which also means that any unsecure javascript or flash that you install will possibly compromise your blog.
The thing to remember with self-hosted blogs, is you are responsible for all updates, all troubleshooting, all backups, etc. Here that is all taken care of for you.
There is also the cost. The combined cost of hosting and the domain registration can run anywhere from $5 per month to $25 per month depending on the host, the package you buy and the amount of bandwidth you need.
Some good hosts are listed at http://wordpress.ORG/hosting/ and personally I use the Tiny shared server package from A Small Orange which is $25 per year, which gives me 3GB of bandwidth which is good for around 10,000 page views per month. The more complex your site becomes, or the more feature rich the theme you use is, the more bandwidth it requires, so the 10k should only be used as a very general guide.