Content Sharing
Content shared on Twitter is likely to always be different than content shared on Facebook. Twitter only submits text posts, while essentially all forms of media can be posted on Facebook.
Advertising
Facebook's advertising business is largely based on targeting users according to information they declare in their Facebook profile. Currently, Twitter profiles contain sparse biographical data and basic follower/following statistics. Twitter's business model is unlikely to be based on profile targeting.
Identity Platform
Recently, Twitter launched a competitive product to Facebook Connect called Sign In with Twitter. So far, Facebook Connect has been implemented by about 10,000 websites, desktop and mobile applications, and most recently, video game consoles. In order for Sign In with Twitter to gain market traction, it's going to have to continue to prove itself as a reliable identity system even though many users are hesitant to share more sensitive personal information.
E-Commerce
Facebook is in the process of alpha testing a payments system built on top of Facebook identity. In the future, it could spread its payment platform across all websites which connect to and rely on Facebook identity through Facebook Connect. Twitter is still a ways off from building its own commerce system on top of the Twitter platform, but interesting payment applications are starting to develop on top of Twitter like we've seen on the Facebook Platform for the last couple of years.
Summary
Facebook and Twitter actually look like pretty different products and businesses today. Twitter is a hybrid broadcast/conversation communication platform, while Facebook is an identity platform with communication,
content distribution, and financial applications built on top of