Are Facebook apps profitable?

I see a lot of people here saying FB is not nearly as profitable as google (one said FB ads pay on average 1/3 of google) and that FB is better to get people to your other sites/apps where they click on the ads there

But what about FB apps? you know apps like games and such that run inside the browser and inside the FB tab. Can you place any ads there or only FB ads?

What are the conversion rates? is it comparable to mobile or we are talking much less?

Thanks