What did Facebook do?
As you may have read already, Facebook announced and limited released their Graph Search. This search may end up being great since two ex-Googlers led the effort; who knows more about search than Google? Probably no one. Basically, Graph Search search is for the four "pillars": People, Photos, Places, and Interests.
Since Facebook has the personal information of millions of users, it's taking advantage of it since Google does not come close to the amount of personal information and photos. While Facebook does have "Likes" of most of their users, this information can be highly inaccurate since many (majority?) of its users don't frequently update it. I know I haven't updated it in years and I don't actually "like" things that interest me. But after taking a look, my interests haven't changed much but many things are missing. Luckily, I'm not one of those users who "liked" everything possible like Coors Beer, your pinky toe, and Facebook pages that only post memes. If that said, Graph Search is just like any other feature, it will only work well if users are active on the service. The potential is definitely there, it'll be interesting to see how users respond and use it; maybe many more two degrees of separation will turn into direct relationships, further decreasing the universal number of degrees of separation.
A few months back Google implemented a feature that is similar to a dulled-down Graph Search. With "Personal Search" results, you get results that included Google+ pages in a regular Google search. But it doesn't just include Google+ information, it uses your browsing history to predict better and more useful results. This is information that Facebook does not current have, dynamic information about their users. Google has taken advantage of this in what seems to be all their services and uses Google Now to exhibits its power and potential. If you haven't used Google Now, you are missing out on one of the best applications I have ever used.
One thing announced last week by Facebook was being able to pay Facebook to talk to high profile people that you are not connected to. For only $100, you can message Mark Zuckerburg who probably won't care what you have to say! Though your message will go to a priority inbox instead of a "Other" folder. The pricing scheme seems to be based on how influential/famous you are. For those who would like to talk to me through Facebook and not friends with me, it's going to cost you well over $100. For most users, this is going to be as useless as their "Promote" pay service.