I adore Lara and the Tomb Raider series (well, at least the earlier games). I was excited to try the PSP version, but I had a lot of trouble with the controls. The sensitivity of the stick was just not what it needed to be in order to play the game smoothly.
I finally traded in the game for the PS2 version, and I am so happy that I did. The controls are smooth and I quickly completed beginning levels that were giving me great grief on the PSP. So if you're on the fence between the PSP version and the full console, I would recommend going for the PS2 version. Not to mention getting to see the fantastic scenery on a large screen!