The difference between Facebook and Twitter can be described in many different ways. If you prefer either service, you might not agree with all my points and defend your preferred social network. Whichever you choose to use, if not both, it all depends on your personal preferences and on the purpose you use it for.
Friends – Followers
The first point of difference is that Facebook is a network to reconnect with friends and family. The people you connect with are mainly people you know, either personally or through other channels. By default friends need to be approved on your personal profile page.
Twitter is a network where anyone can follow anyone. People who like what they see on your page can simply follow your tweets and there is no need to approve anyone by default. This means that your network is less personal and has a much broader range.
Facebook offers features like email, instant messaging, image and video sharing, etc. and feels familiar. It is easy to find your way around Facebook when you first join and it can become quite addictive as you can browse your friends pages, their photos etc.
Twitter on the other hand offers 140 character micro blogging sharing, private messaging and has started using affiliate sites and applications to upload and share photos, they are however not stored on your page. Twitter is more of a portal to jump to other places through strategically placing adequate links.
Personal – business
Where Facebook is more about sharing from a personal level with people you know (just looking at the personal profile page), tweeting is especially used by anyone with something to promote: bloggers, online marketers, etc.
Twitter is also used to ask questions and get instantaneous responses from people with whom you might otherwise have no connection. Twitter is a platform to put yourself out there and to self promote, whereas Facebook is mostly used to chat with old friends.
Facebook versus Twitter
As mentioned in the first paragraph you will most likely have your favorite. The truth is that both have their advantages and disadvantages and it totally depends on what you use it for. In the end, both are social networks, which will develop over time, using user feedback and updating with new inventions.
If you are using them for more than personal pleasure you will look for return on your investment of time, whether that is through Facebook or Twitter or potentially a consolidated version of the future.