We tried with both Tweet it or Share on Facebook. 83% people clicked on tweet it only button. 12% clicked on both and rest 5% on Share on FB only. All the new users that we got from this "Got_Followers" social sharing where from twitter only. Yes, zero converted from Facebook posts. Hence, we decided to stick with twitter only.
Another test we ran on our Facebook page (http://facebook.com/pinwoot) was to have a tab called "Try Now" which was basically connected to our Facebook connect app - that was great, many many conversions. So, we are still using it.