Did you know that Orkut & Facebook were launched almost at the same time ? Orkut was launched on January 22, 2004 & Facebook on 4th February 2004.
A Google engineer named Orkut Buyukkokten, developed Orkut as part of the 20% time granted by Google to its employees to work on independent projects. Mark Zuckerberg launched Facebook from his dorm room at Harvard .
Orkut was the dominant social networking site until Facebook surpassed it to take the top position. As of September 2011, Facebook had more than 800 million active users. Whereas, as of October 2011, Orkut had only 66 million active users worldwide. However, in December 2006, Facebook had only 12 million active users & Orkut had around 30 million users(October, 2006) .

We can see that the growth of Orkut has been dormant. So, what was the reason for the decline of Orkut vis-à-vis Facebook ?
Although Orkut is less popular than Facebook in the United States, it is one of the most visited websites in Brazil (58 % of users of Orkut) and India( 32% of users of Orkut). However, Orkut is popular only in some countries like India and Brazil while Facebook is popular among people all over the world.
Orkut, required an invitation to join till October 2006. This invitation was one of the reasons behind Orkut’s failure to compete with MySpace. Facebook became invitation-free in September 2006.
According to me, the following reasons, led to the decline of Orkut & growth of Facebook:
1. In August 2008, the operations of Orkut shifted to Brazil from the US. This was done due to the large number of users in Brazil & cropping up of legal issues in the US. However, Orkut’s popularity sharply fell in 2010, when most users in Brazil & India switched over to Facebook.
2. Facebook allowed any developer to develop applications from the beginning & there is a active & vibrant Community of Facebook application developers.
3. No doubt, Facebook is a better product than Orkut. Facebook has better features than Orkut & there are regular upgrades to it. Facebook also has a better User-interface than Orkut.
4. The Social gaming apps like FarmVille, FishVille, Mafia Wars, Sudoku and others helped Facebook beat Orkut.
5. Orkut does not allow User profiles to be indexed by Search Engines . May be due to this reason, it was impossible for you to find lost friends in Orkut, through Google. This may be one of reasons, why Orkut lost lot of Web traffic & hence users (As you know, around 40% of users arrive at any website through Search Engines).
However, the User profiles of Facebook are indexed by Search Engine Spiders. I have found a lot of my lost friends through a Google search result which was directed to User profiles in Facebook. Ironically, the whole idea of not allowing profiles to be searchable in Search Engines was to protect privacy of users of Orkut.
6. The only way to get noticed in Orkut is by putting your snaps. Facebook on the other hand presents you with ample of opportunities to be noticed. You write on your wall, which is liked or commented upon. The comments and like tempts similar people to do the same.
7. I am not aware of a single celebrity who has an Orkut account. On the other hand, there are tons of Celebrities who have a Facebook page. So, today it’s fashionable to say “I am on Facebook”.
8. One of the reasons for the decline of Orkut was privacy issues which even led to legal tangles. However, Facebook kept fixing their privacy issues, as they arose.
I do not think there is a question of preferring one over the other. There are lots & lots of people who still have accounts in Orkut only & and not in Facebook. I still, use Orkut as many of my friends are there. If they stop using Orkut and start using Facebook, I will also go ahead and do the same.