Well at least for now the winner of the battle within search engines for which has more effect on ranking is links. The source of this information to me is both through talking to other people in the industry and reading lots of blogs. That today was added to when I saw this youtube video of @mattcutts talking at SMX Advanced in June about this subject. [youtube https://www.youtube.com/watch?v=mXJylyR2Lc0&w=500&h=375]
In essence the take away is that social is big and its growing but right now it's not having a huge influence in search rankings. The democracy is still being led by links, but social influence in the next few years may take the lead.
Where will the battle go in the next few years? Will links remain supreme or will social take over?