I'll make this short for now, at least. I'd never played a Tomb Raider game (though I own Anniversary and Legends for PC), but this was decent.
I wanted to use mouse+keyboard, but the mouselook probably would have given me a headache, so I used a 360 controller since the camera rotation on it was much slower/smoother. The camera was still pretty jerky and hard to get where you wanted it, often...it's nice to be able to zoom in on Lara, but sometimes I'd like to see other stuff, like where I'm jumping.

Not being able to use the handheld camera OR look through Lara's eyes when you're on a wall is annoying.
Prince of Persia sands of time seemed to have a much more fluid system for jumping off stuff (you could walljump or wallrun on all KINDS of stuff), as well as multiple camera modes (through the prince's eyes, the normal camera, the really zoomed-out camera). I think having that kind of stuff could have helped this Tomb Raider.
I also would have liked some more detailed graphics options like low/medium/high, instead of just on/off, but I'm probably spoiled on graphics from stuff like Crysis Warhead. I don't know what fps I was getting (that would have been nice as an option on PC too...and motion blur could have helped some stuff probably), but I felt like 2xAA and 2xFSAA ran quite well on an e8400+ATI 4850 512MB, but 4xAA+4xFSAA didn't run as well. I left triple buffering off and everything else, including vsync, on (I don't know details on triple buffering). Ran at 1680x1050 fullscreen.
The environment was pretty, and I really liked the sound, though. I turned off all the hint text and button press cues, and it was fun to try to figure out the puzzle. I fell into the giant pit, though, so now I'm going to have to look up how to get further than that in the demo, via that video posted earlier...
Want to get the game.
*edit* Oh, one more positive note: Ran very smoothly on Vista 4GB RAM, and I alt-tabbed back and forth a BUNCH...never had any problems or crashes changing graphics options and switching around. There are graphics issues like objects clipping, and unrealistic stuff like Lara bouncing when she hits the ground, but it's overall decent.