Facebook may be a much bigger social network than Twitter, but when it comes to realtime search, Twitter is far superior.
There's been plenty of speculation that Facebook could one day enter the search market, and compete with Google on the search front. We've contributed our fair share of this speculation. I'm not going to rehash the whole argument here (I did that here), but a recent study indicates that Facebook could have 22% of the search market right out of the box, if a Facebook search engine launched.
With the company being public now, the speculation will no doubt only continue to come out of the woodwork. Facebook and Google are going to be competing more and more in advertising and social media, so it seems logical that Facebook eventually tackle search in a more direct way, especially considering that it has some very valuable data about web users (over 900 million of them, apparently), which Google simply does not have access to, despite its increased efforts to inject social into search.
There is a lot of potential for Facebook in search. However, it's just that. Potential. Right now, Facebook search is next to useless, unless you're looking for specific people, pages, apps, groups, etc. Searching through public posts is pretty much pointless right now. You can probably get more out of a "site:facebook.com facebook ipo" Google search.
This morning, I searched Facebook's public posts on Facebook for "facebook ipo," hoping to get a feel fro what users have to say about it. Facebook lets me see close to 30 updates at once - probably not the best representation of the entire Facebook user-base.
Compare that to Twitter search, where the updates roll in faster than I can read them.
Obviously, Twitter has the edge because it is public by default. Most tweets are available for anyone to see, but there is a lot of Facebook content that is public (granted, Facebook's searching posts by friends is where it holds greater value to the user), and Facebook simply doesn't let you seen more posts at once. You're simply left to hope the ones Facebook is showing you at any given time are helpful to your query. It's not like Google, where you can just click through various pages.
As I saw someone else point out, you can learn a lot more about what people really think about the Facebook IPO from Twitter reaction, rather than Facebook reaction.