I prefer Twitter because it's easier to engage in conversation with people. It can also make you famous! I got a retweet from Wil Wheaton last night and I got quite a few followers from it. Facebook is more of a social thing you do with your friends, whereas Twitter is just an all-round microblog.
One of the things that annoy me about Facebook is all the people sending me annoying Zynga game requests. I don't like FarmVille or any of that nerdy simulation rubbish! Also, updating your Facebook status too often makes you feel annoying. That's what Twitter is for; even though there's a 140 character limit on tweets, it's easier to get your word out with hashtags, mentions and retweets.
If you run a Facebook fan page, it's not easy to reply to comments. You could comment something, replying to someone, and have it pushed away but the hundreds of people who will comment afterwards, probably not being seen at all. But on Twitter, people can check out your profile, see who you're talking to and maybe give their opinion. It's all easily accessible.