Okei, played a few hours of the PS3 version yesterday at my university, so here are some quick impressions (this will be messy):
(I'll preface this by my tastes on similar games - I loved the original Tomb Raider trilogy back in the day, particularly 2. Didn't enjoy 4, Chronicles, AoD or Legend. Enjoyed Anniversary and Underworld. Liked Uncharted 1, adore Uncharted 2, disappointed in Uncharted 3).
It looks wonderful. Like, really. I'm playing on the PS3 version, so I'm not sure about the Xbox version, but it runs well (few framerate dips here and there, minor). I'm honestly extremely impressed with the graphical quality. The island is extremely atmospheric. Rain soaks the environments, thunderstorms and lightning strikes illuminate dank alcoves and caves, and Lara's model herself is extremely detailed. I'm excited to see this game on the PC.
It's Uncharted. I don't like to redact it as such, but I mean it as a compliment. Will individuals who enjoy the early Tomb Raider's a lot be disappointed? Hard to say. I love them, yet I can accept this is a different type of game now. Regardless, it's not 'Uncharted-lite'. It is of equal quality (surpassing Uncharted 3 for myself, as I was greatly disappointed in that after the second game). Early game focuses on survival - finding shelter and camp, learning to use your equipment and bow, etc. Each section you enter is more like a large hub. They are all connected, however, and hide secret treasures, diaries (voiced) and tombs (yay!). You will go off the beaten path, more so than you ever did in the Uncharted series.
The gun(bow)play is smooth. Extremely smooth. The scramble motion (circle button) is a great feature which adds to the sense of tension and uncertainty. There is cover, but it's not sticky, you merely approach some form of cover and Lara will align herself correctly. Very easy to move in and out without getting stuck like in Gears or Uncharted.
There are upgrade paths. You can reinforce your bow strings for faster shooting speed, create stronger axe's, etc. There are also skill points, which allow you to upgrade either your survival instincts (scavenging for food, supplies), your hunter abilities (combat abilities) and personal or strength or such (health, etc).
The story is engaging so far. As I said, I'm only about 4 hours in, but so far there has been ample amounts of mystery and intrigue about the island, it's inhabitants and the supporting cast. The music and sound effects are phenomenal. I'm a bit of a sound freak, so I'm usually greatly disappointed in games that don't take full advantage of these areas. Not so with this. I advise anyone to play with headphones, as little details such as dripping stalactites in caves add so much to the atmosphere.
That's all. Apologies for the info dump, it's the best I could do right now. Any questions about the early hours and I'll try my best to answer.