By blogging about your interests, by sharing news, links and photos, you are helping explain to the world who you are, what you like and don't like, what you represent, and what you do. If you choose to break news or comment on the day's news, you are doing so through a personal filter which covers everything. If you choose to talk about sports and technology, your choices as to what you want to discuss help define your brand. And, more importantly, the quality of your posts, the frequency of your posts, the length of your posts, all those elements help to illustrate your writing abilities, your attention to detail, your ability to stick to a project, and comprehension or adoption of new technology.
A personal blog will always be much better as a brand than your Facebook profile or LinkedIn profile.
A Facebook profile, even with the newest enhancements to the service, shows photos, groups and networks you consider yourself part of, the friends you have, updates you provide, applications you have installed, and a short message board, or "wall". But the Facebook profile does not allow for much personalization of look, feel or content. The Facebook profile doesn't allow for post after post of prose. The Facebook profile allows you to show how you're connected to a friend, but doesn't give you a platform to talk about the relationship. The Facebook profile is not your brand, but instead the Facebook brand with a small helping of your content.
Your LinkedIn profile is an excellent business card and resume, with job history, relationships, and recommendations. But it is not your brand. Instead, it is one, strong, contributing element to your brand.
As important as it is for me to look to LinkedIn and Facebook to know about a new hire candidate, or to research acquaintances, a blog will go far beyond in explaining to me how this person wants to be portrayed. I now expect job candidates to have blogs, and make that part of the interview process, whether it's related to their position or not. Even if the big shots like Steve Rubel of MicroPersuasion and Robert Scoble are successful in moving microupdates away from their blog and to other services, their blog will be the best measure of their personal brand to me, and should not be abandoned, because no other single service can best be owned by and represent the individual.