Played this quite a lot today, and my 360 didn’t crash at all. Which is most odd. The game did glitch once though – I fell down a hole, but Lara’s death scream never happened, the screen went black, and I could still shoot and bring up the inventory, but not do anything. Very strange.
As for how I did today, I killed the T-Rex (without dying, so got an achievement for that!), completed Peru, and have just reached Midas in Greece. I remembered the four gods bit of Greece and the final few bits of Peru from the original game, but everything is the same… only different.
Oh, and I’m playing on Hard for no reason other than I thought I’d give it a go. So far, I’ve not had much difficulty in terms of killing things, so I’m not sure how hard easier modes would be.