This has been quite an easy "thing" to do as I'm already on both these social networking sites.
Joined Facebook first and love it. It's good to be able to share news, photos, etc. with family and friends. A lot of it is rubbish and you have to watch out for scams but generally I would miss it if it wasn't around. That said, it's quite nice to go away occasionally and have a complete break.
I also like the way you can pass on information about events (or even organise them yourself), participate in various groups, make comments about all sorts of random things ... and some of it is genuinely amusing!
Twitter I joined at a later date. Was a bit wary at first as it's so public (and yes, I know you can make it private but there doesn't seem much point) and you are always hearing horror stories of people's tweets or unfortunate photos going viral. But I was at a conference and wanted to "join in" with tweeting so I signed up.
I tend to use Twitter for more professional things, putting links to reports, making comments about books, reading, libraries, literacy ... although I do occasionally throw in something more personal but I figure that people following me are doing it because of my librarian connections and aren't really interested in my latest knitted creation or fantastic food I've just eaten. I also retweet professional stuff ...
Whereas my Facebook is a real mix of personal, professional and my obsessions ...
As much of what I tweet I would also like to add to my Facebook page (a lot of Facebook friends are library/book related ... and even if they aren't then they all know I'm a librarian so these sort of comments wouldn't be amiss), I have set things up so that any tweets go straight to Facebook ... saves me having to do it twice!
Regarding both these platforms, I find the amount of information on them staggering and it's so easy to miss things if you're out of the loop for a couple of days. No wonder people become hooked on them! You also really could waste half your life away reading comments, watching YouTube videos and doing quizzes (now then, must try and get to the next level of Candy Crush before I sign off tonight ....).