Google vs Facebook? I don't think so.
Just finished reading this article on the internal economy of Facebook. Mostly it is about Facebook's growth struggles and how recent changes in layout have hurt the businesses of lots of Facebook App Developers. But one small part was about Facebook's place in the larger web ecosystem.
The Article maintained that Facebook aims to be the OS of the Web, "making the web fundamentally social across all sites and applications." In this, it competes with Google.
"Google says the modern day operating system, or at least the starting off point on the Web, starts with search. Facebook believes it starts with people connected via social networking." ~Developers Struggle Amid Fragile Facebook Economy
This reminds me of my thinking about the web ca. 1995. There is a basic truism about the internet. People get on the net to get stuff done or to mess around. Save time or waste time. I think maybe 'search' is weighted towards saving time, and web 2.0/social apps are weighted toward the waste time end. So, Google and Facebook aren't even in the same market. Folks aren't going to get on Google to check in with their friends and they aren't going to use Facebook to find a grant for their non-profit or to search for a part number.