Facebook is profitable, yes. Most of people (edit: instead of most I said '99%' but that's not true so I updated) use FB from their browser going to facebook.com (or searching facebook on Google and clicking the first link), while Twitter is used mostly in desktop/mobile apps.
It's a bit more difficult to develop a business model for Twitter than for Facebook, which is profitable with "just put ads on the right of everypage".
But: shouldn't a company as huge as FB be many times more profitable that they are right now? (400M$ in profits in 2010: http://dealbook.nytimes.com/2011/01/06/goldman-unit-passed-o... at a 75B$ valuation if I recall correctly).
Anyway, my point is Twitter & FB business models are not & i'd guess won't even be similar, and it'd difficult to compare them.