I think it would depends on three factors:
For example - Facebook has limited space to say what you want. You may not want to hit your e-mail list as often as you would Facebook. But Facebook updates may not be appropriate for LinkedIn. Etc...
Your blog would give you the most flexibility and should probably be your primary outlet. People can always subscribe to the feed to get an "e-mail like" update when you change it. Facebook can be used for quick updates and link to the blog when appropriate. Perfect for people who don't like to read much, but want to keep in touch. Reserve LinkedIn for information that is directly related to your product or service. And finally, your e-mail newsletter could be a monthly summary of all of the above.
"He was a wise man who invented beer. -- Plato"