In India 2001, all good knocks but 1st innings with less pressure. Even the 1st test, it was Gilchrist who stole the show after India were shot out for a low score.
SA 2002, good knock again but arguably the worst SA attack ever and had some nice support.
Gall 2004, yup a very fine knock under pressure, I agree.
Oval 2005, this is a strange example since this knock is used to criticize him. It was a good batting pitch but he batted unusually slowly to save his career, and he and Langer strangely took the light after tea on the second day which killed time in the game.
2006 SA, good knock again but was this really a pressure situation? SA were shot out cheaply and not a particularly great attack.
Anyways, the point is not that Hayden never batted under pressure, but that his best usually came in dominating the opposition relentlessly, which is still great. I would say that Langer, though not as good an opener overall, was a better pressure player than Hayden.
Whereas with Smith, you had several knocks where if he didnt score in those situations, SA would almost certainly have lost.