Ah, as someone who owned and reviewed all versions of Staff of Kings I'm the one to help you out!
Overall the easy answer is PSP. The story is actually told better in this version, John Armstrong does a much better job as Indy and narrates the plot, you get to experience his falling out with Magnus, and his arguments with Maggie O'Malley give the emotion that was lacking in the Wii/PS2 version. Even the graphics are better! Controls are a little bit Emperor's Tomb style and work fine for me.
HOWEVER it is NOT a long game by any stretch of the imagination. Stages are incredibly short and most can be finished in a matter of minutes, with the whole game clockable in about 1-2 hours. There are extras to discover and challenges to overcome, but don't expect a long game from the PSP version - or stages that take place over more than one room.
The DS version is more basic-looking but is a bit more of a proper game.
Of course, this is all mostly for anyone else looking into buying these games since you've probably long since finished them all!