LinkedIn is primarily business oriented. It was originally conceived as a way for people to "network" with their friends for finding job opportunities. And it still works very well for that purpose. But it can also function as a Family/Friends network as well, it just wasn't designed with that in mind.
Facebook on the other hand evolved as a Family/Friends network, but then as people started creating "pages" to represent their entrepreneurial endeavors (businesses), Facebook began to morph into a marketing medium for businesses (and that's when it took off).
Now for both of these services (and for many others who want to emulate them) the mere value of containing "the network" of members is producing business revenue, so the nature of these services are changing to exploit those new markets.
Bottom line: If you just want to be chatty with someone and talk about personal things, I would use FaceBook. If you want to use your business associates as friends to help you find a new job, then I would use LinkedIn. And if you have a small business or a hobby that you want to market, then I would create a "page" on FaceBook.