Facebook leaves more room for detail than Twitter and has the option to include supporting images. You can explain what Thunderclap is and why people should support your message. By "priming" your audience, you’ll get a much higher percentage of opt-ins than if you were to simply drop a link on your page. Push out at least one or two Facebook posts per day and experiment with different wording to see what works best.
Facebook invites and shares allow you to display more content and imagery than you can on Twitter.