Being a private person I remember back when I made my facebook page I used the name of one of my old DAoC characters. The entertaining thing is I've gotten about a dozen messages over the years from people with the surname from, apparently, South America looking for relatives with the same surname. Funny stuff. I think I preferred the old screen name internet days to the days where so many people seem to use their real names, especially when it comes to some of the kids you see that have all their information public. There are just so many ways for that to go wrong.
My worries about information privacy aside, there's no discounting the speed facebook can provide information at. Still, out of the two of them.. I think I prefer twitter. It cuts out a lot of the fluff I never use anyways, and gets to the core of what I do use.