The best thing about Twitter is the real-time search and it's insanely useful when you are having trouble with something and you want to find out whether it's just you. Facebook on the other hand doesn't provide search, but Google Plus does!
Visit GPlusSearch.com, and do it. You can search from all public data on Google Plus like posts and profile details and also stuff on Buzz and Google Reader. The website is not by Google itself, but it uses Google Custom Search to provide queries.