In fact, I seem to recall reading recently (Wikipedia confirms it) that Sochi, somehow, has managed to break Beijing's record for most expensive Olympics ever - and for Winter games with half the events if not even less, that's really sad. It seems to be a combination of the bizarre choice of venue, forcing Russia to build just about all infrastructure from scratch, and the boundary-pushing levels of corruption with roads to nowhere and whatnot. Which leads one to suspect that at the end of the day the people of Sochi won't necessarily have that much left after the games from all those huge investments made.

Russia still has plenty of gas money to spend on prestige projects, just like China does, and right now the Russian GDP per person is still comfortably ahead of China's. For how much longer, that's another question. The difference is more that the Chinese authorities seem much more concerned with their reputation, both in the eyes of their own population and in those of foreign countries, and keep a much closer lid on corruption or really blatant abuses of power. Putin doesn't give a damn about how people see him, as long as they respect his strength. And that, I suspect, is why you're inclined to see Russia as a 3rd world country more than China even though it's nearly twice as rich on a per capita (PPP) basis.