I finally figured it out. I may be the last one, but I am a little slow, so bear with me.
Facebook allows for cross-posting your tweets to FB, but it's pointless. If I follow you on FB, I don't need to see the same posts on Twitter and vice versa.
What I have come to realize is that Twitter and FB updates have their own unique purposes.
FB friends are people I know in real life (for the most part), so those updates can be more personal.
On Twitter I am followed by many people I've never met. They could (presumably) not care less about what I'm eating for dinner, how much I love my new shoes, etc. (Of course, it is debatable as to whether my FB friends care either, but that is a different story.)
After the election I stopped using Twitter for a while because of all the duplicate posts. I loved watching the debates with Twitter, but after that, my interest waned considerably.
Now I have it figured out. Twitter is useful to me for one thing only: discussions about toics of common interest. Topics may include news, conferences, movies, beers, restaurants, brands, etc.
Twitter is a public forum. If I tweet about the Beer Wars movie, people from around the country are going to soon search on "beerwars", see my comments and those by everyone else tweeting about the movie. It's a shared experience like nothing else I can think of. And, actually, it's pretty fabulous. I'm all fired up about Twitter again.
And now I'm going to unfollow all of my Twitter friends who cross-post to FB. It's nothing personal, guys. If you decide to separate the two, please post a message on FB so that I can start following you again.