My personal "solution" is that I typically share personal stuff exclusively on Facebook (non-public posts) and what is more "technical" (comments or questions on tech, products, etc.) on Twitter. (and HN)
For example, I didn't announce the birth of my daughter on Twitter, because I've known the people who follow me in mostly professional settings. Some of those might be friends too, but if they are, they're probably on Facebook too.
Works well for the most part, except when I'd be interested in the opinion of Facebook friends that are not on Twitter… But it won't work for everyone either.
I realize that it's possible that I am missing out on opportunities to create stronger personal relationships with people on Twitter by not discussing personal matters there, but that's honestly getting too complicated. :)