This battle will come down to productivity. In the world of email, search and portable documents, Google has held the throne for more than a few years. In the world of making connections, Facebook has been the primary provider of highly productive online social networking. Facebook's ease of use, coupled with the stability of having your searchable username be the same as your real name, have turned it into the premier site for your general personal social networking needs.
Google's success in search, Gmail, Docs and news has been a result of the productivity and efficiency of these services. It only took 2 seconds for any user to realize that Google Docs was a good way for them to collaboratively work on text and spreadsheets, because it was highly usable, and conveniently available for anyone who held a free Gmail account.
It would be easy for Facebook to develop an email platform based on their username. The question is whether that would prove useful for people. Personally, I think it would be unpopular and ineffective. It's easy enough to "Send a message" to your friends through the Facebook interface.
As for Google, there is real potential for a social networking revolution based on search. Imagine if your online profile through Google automatically brought up top search results on what was going on with your former classmates? Or if your work history automatically linked your profile to your former coworkers? The result would be a much-more-accessible online social network, especially if Facebook networks became searchable.
As many commenters have mentioned, one touchy area would be privacy. I'm particularly interested in the visibility of a user's profile. If Google search results become more attuned to individuals (by their real name) "à la Facebook", then any "private" personal data will be available to everyone.
This will spark at real shift in mentality among the users of social networks. Erasing or "desocializing" one's Web 2.0 identity, either through making requests to Google or/and going site-by-site to eliminate private info, will become as common as running spam blockers. Searchable Google identities will wake people up to the reality of "online privacy".
But "Google IDs" would certainly be a hit, because it would make us more productive in our day-to-day life. Need a job? Google's webcrawlers can help you find one. Want to find your buddy from that summer camp way-back-when? Someone probably updated a group photo and tagged everybody (and though your old buddy doesn't have Gmail, he leaves a cybertrail that's easy to follow). Want to know how many of your high school classmates hit the big-time? You would probably be able to search it in one query (although your dashboard will probably have already given you a clue).
