Yahoo! is now competing with Facebook Connect. Through a partnership with JS-Kit, Yahoo! Updates is now available on over 600,000 websites. The joint effort helps sites bring social networking functionality to their sites. (Google's Friend Connect is also a player in this space.)
Meanwhile, Facebook is competing with Twitter. It had been rumored that Facebook sought to acquire Twitter, but the deal fell through (apparently because Twitter wanted to go after search). Now, Facebook is going after Twitter by adding more live-stream features to their network.
Last year, Facebook updated user profile pages and the user experience, focusing on streams of updates by friends. Now, public profiles and organizations are getting pages that look more like user pages. The focus, again, is on the real-time stream of updated information.
Additionally, Facebook is updating their home page with the live-stream concept in mind. The new home page will begin rolling out next week. In the meantime, here's a preview: