Facebook isn’t just winning the battle for web users’ time (comScore says Facebook passed Google this month), they are also pulling some of Google’s star engineers.  Google (GOOG) has been offering huge bonuses to retain some of that talent but the bigger battle is getting the Google behemoth to be more social.

That’s where Google is headed according to CEO Eric Schmidt who spoke yesterday Google Zeitgeist conference in Scottsdale, Arizona.

“We’re trying to take Google’s core products and add a social component.  If you think about it, it’s obvious. With your permission, knowing more about who your friends are, we can provide more tailored recommendations. Search quality can get better.”

Although he downplayed copying Facebook’s functionality directly, he made no bones about wanting Google users to have the same sort of Social Graph that Facebook enjoys.

How does Google intend to acquire that information?  Google already has a great deal of connections information in Gmail/Google Talk/Contact/Buzz/YouTube databases, but it isn’t nearly as clean and polished as Facebook’s.

Surprisingly, Schmidt said they planned to get more of that social graph directly from Facebook itself:

“The best thing that would happen is for Facebook to open up its data,” Mr. Schmidt said. “Failing that, there are other ways to get that information.” He declined to be specific.

Cue the Microsoft-funded Consumer Watchdog group with another cartoon Schmidt saying, “We have ways of making you talk, muhahahahah”

Facebook isn’t just going to hand over their user’s social graph just because Google wants it.  They are going to make it a little bit harder, I’d imagine.

Ultimately, Google and Facebook users will decide which bits of connection information is shared. If Google creates a compelling case, as Facebook has, of entering it in manually, consumers will populate Google with their social networking information.

I like that Google has started dividing connections up into groups (Family/Friends/co-workers/etc) in Orkut. I think that is an important differentiator going forward that Facebook needs to embrace.

Schmidt also downplayed the idea of a stand-alone Google Me product, saying “Everybody has convinced themselves that there’s some huge project about to get announced next week. And I can assure you that’s not the case.”