The essential difference is that if you want to see what someone is up to onFacebook, they have to approve your request and then they see what you're up to - it's a symmetric relationship. Thus, it's only really useful for talking to your real-life friends. If your real-life friends don't use it, there's no point in joining (unless you're going to convert them to it, but why would you?)
Twitter works differently in that you can follow anyone you like and they can follow you back or not, as they feel. This makes it a lot better for following famous, witty or erudite people who you don't know, even if you're not famous, witty or erudite yourself. On the other hand it's (at least presently) not nearly as good for extended conversations about nothing as it doesn't show the thread of who said what in reply to what.
So, on twitter I can find out what Ben Goldacre thinks about libel reform (a subject which interests me but of which I don't have enough knowledge to say anything meaningful myself), on facebook I can find out what my friends think about the pub quiz last night.
I've oversimplified somewhat (facebook has fan pages and twitter has the option for protected updates, so it is technically possible to use each for what the other is more usually used for) and I've left off mentioning the annoying games, quizzes and adverts on facebook, but that's the basics as I see them.