LinkedIn is an excellent place to post a virtual resume and connect on a strictly professional basis with people in your field. It tends to be a way to connect with peers. It has a few applications, but not many, and all are business-oriented. For instance, you can pull in a feed of your blog or Twitter stream, if you have them. There are also groups you can join to keep up with your industry.
Facebook is better for posting regular updates to a wider audience. By creating a business Page on Facebook, you can reach a wide potential client base, customers instead of peers. Facebook also has a huge assortment of applications to choose from (some more professional than others) and as such can be very powerful.
I tend to think of LinkedIn as better for professional promotion of the individual, while Facebook is excellent for promoting an organization.