Facebook is the winner by a landslide, but not for the reasons you think
Facebook is the winner by a landslide, but not for the reasons you think. I can produce more links from Twitter for myself, but I can get more high quality links produced by others from Facebook. Stop and think about that for a moment.
I engage with clients more closely on Facebook than on Twitter due to the more complete platform. You can share videos, pictures, stories, events, and other items on Facebook that are not as persistent on Twitter. When you do it right, your readers share you content on their Facebook feeds, on Twitter, on their blogs, and in other social media outlets. You get more overall links by focusing on quality content through Facebook than by building links though Twitter.
Real engagement takes more time, but the results are worth it.