You know you can cause all your tweets to automatically appear on FB and vice versa, right?
Twitter to Facebook – details here. (while giving FB posting permissions, make sure that the tweets appear on facebook to a limited audience – say friend or friends of friends to avoid a feedback loop in case you setup FB-> twitter posting)
Facebook to Twitter – Just set up public posts to be tweeted by going to https://www.facebook.com/twitter
If you automatically share from WordPress to Facebook and Twitter – beware that the FB<->Twitter syncing will cause a feedback loop. Rather, just sync with one of them.