This seems to be the topic of today and from what I can gather, most people think Facebook is going to win out. I have to agree somewhat, but I don't think it will be as cut and dry as some are advocating.
Google provides a generalized search. The fact that google have links to site search boxes (even youtube, one of their own products) within their main search results is testament to the fact that when it comes to niche areas, they can't (yet) organize and search through information better than everyone else. I'm sure that won't stop them continuing towards that goal but nonetheless, they currently can't compete on search result quality with these "niche" sites using their current monolithic search infrastructure.
Facebook provides aggregation of data. This is not search. This is not replacing search. It's a relatively new Internet phenomenon that is increasingly taking up more and more time online.
As generations become more familiar with the internet, "google.com", "gmail.com", "myspace.com", all become second nature. We don't need to use search engines to get to these sites. As the social web expands, users on one site will tell us about other sites and we don't need sites like google to tell us where to find things.
Google is therefore transforming into a first point of contact for anything you don't already know. Anything you do already know, you can generally already find. As we spend more of our time on social sites, I can't help but think we'll continue to rely less and less on sites like Google but I'm not sure there is a "fight" between Google and Facebook, and I certainly don't think Facebook is going to end up replacing our favorite search giant.