Let me start this off by saying I can't compare this game to Tomb Raider: Legend for the PSP since I have not played it. That being said, I found this game to be extremely fun, and I was pleasantly surprised at the high graphical quality that was pulled from the PSP hardware.
Now, to get the bad out of the way first. Like Tomb Raider: Legend for the multiple consoles it was released on, the fighting mechanic isn't great. It's by no means unplayable, but then again Tomb Raider is a game that is more focused on exploration and platforming than on gun play.
One of the first questions that will likely come to mind to anyone interested in playing this game will be the camera. If you have played Daxter for the PSP, than it is quite similar, and does not cause much trouble, which is rare for a PSP game. However it does tend to have it's share of problems in the middle of a fight, which tends to be the most frustrating. Not much of a problem though since the enemy A.I. isn't that great to begin with. The Controls are set up as good as can be for the PSP as well, and again will give little trouble.
But it's all about the Tomb Raiding and this is where the game shines. The levels seem larger and less linear than in Tomb Raider: Legend, and again are beautiful to behold. The only down side is that there are technicaly only 4 this time around. Peru, Greece, Egypt, and Lost Island. The developers also added Croft Manor again. The puzzles can be easy at times, and other times leave you stumped, providing a good challenge. If you are a fan of adventure games and don't own this game on any of the consoles, than you will likely enjoy it.
I would still recommend the game on consoles first, particularly the upcoming 360 version, but you can't go wrong with this game for your PSP.