Well, I prefer Facebook over twitter to which I will now tell you why.
Twitter- I will be honest, I have never used Twitter in my life. I don't have an account and I never plan to get one. As far as I know all your posts are public, so anyone can see them. That means you cannot really talk to someone in private. The most annoying thing though is that you have the character limit. 150 characters I believe. That is WAY to short. I usually like saying a lot in my messages.
Facebook- I don't really have anything against Facebook. Ya, the newsfeed thing could be better, but it isn't horrible. The main thing is that you can chat with people and not everyone sees the message. And no character limit.