We're not purists, but while Facebook and Twitter are both social media channels they are different beasts. In our experience Twitter is more about quick thoughts, news, pushing a blog post, responding to other feeds and learning. Facebook is, for us, so much more social, friend to friend and...limited.
On Facebook you can ramble on about your thoughts, photos, experiences but on Twitter you've got 140 characters and that means you have to be succinct.
We think your posts should be separate. When we're watching the Twitter Stream and a FB Post hits...you know that we know...right? And a third of the way through your thought you ask us to head to your FB page.
Better that you create your Facebook Post and then distill your thoughts for Twitter. Besides, and we hate to say it...linking up your FB and Twitter Streams...is sorta...lazy.