Currently I use both Facebook and Twitter. Some of my friends, that only use Facebook, don't see the utility of Twitter. I decided to write a description of how I use Twitter and how it compares to Facebook
I see Twitter and Facebook as tools that do better job at different tasks. Facebook is great for communicating with people that you already have relationships with. While, I use Twitter is an information gathering tool.
On Twitter, a user explicitly "follows" other twitter accounts. This explicitly indicates that the user is interested in the information provided by those followed accounts.
For example, I have "followed" the Starbucks twitter account, so I have indicated that I am interested in receiving the Starbucks "marketing message". This "following" doesn't indicate any personal relationship, and following is not a two way relationship. Starbucks may never see what I say about them.
Personally, I use Twitter for "receiving information that I am interested in". There are several world wide news organizations that I "follow" that often have information about current event significantly faster than the traditional news media. Also, I "follow" several local radio stations. These stations use twitter to send information about traffic conditions for local roads.
Also, the value of any one particular "tweet" is pretty low to me. If I miss a whole day of information, I will not spend the time to catch up on them.
I don't often manually post "tweets" to twitter. I do use some tools to automatically post to twitter. For example, when I want to share an article that I am reading, I will share it in Google Reader or delicious.com, and then this will automatically be posted to twitter. When I write a blog post, this link is automatically posted to twitter
If someone is interested in the things that I am sharing, then they can follow my twitter feed, if not they will not follow my feed.