The big problem with PSP games used to be that all the developers on the planet were either using it for ill-advised retro collections or shovelware that was designed for the PS2. The result was that most games were either unplayable because of the screen or unplayable because of the lack of a second analogue stick.
Now the PSP is getting a sort of second life as a platform for strategy gaming, with Disgaea: Afternoon of Darkness, Final Fantasy Tactics, and the only original title of the bunch, Jeanne d'Arc. Jeanne deserves to be mentioned in that kind of company, too, as it's a genuinely addictive, solid turn-based strategy game.
The premise is the kind of thing that makes Westerners immediately think drugs were involved in its conception; Jeanne, a young girl living in France during the Hundred Years' War, finds a magical armlet. The armlet allows her to occasionally don a suit of powerful armor, but she's also hearing mysterious voices that direct her into battle against the English... who, in this version of history, are fielding small armies of porcine demons.
I bet this game is selling like crazy in the UK.
Jeanne d'Arc's combat system is interesting. If you've ever played a Japanese-style turn-based strategy game before (which is to say, anything from Shining Force to Disgaea), you'll almost immediately be on comfortable ground, with the game being careful to explain new wrinkles of the system at the beginning of each map on which they become relevant. Each character can equip various special moves, and Jeanne herself can transform into a powerful armored form for a few turns, but they can't do so right away. Instead, the MP you spend to use these abilities is gradually accumulated over the course of a few turns, preventing you from unloading a ton of burst damage and skating right through a fight.
Most battles you get into will have a limited number of turns in which you must accomplish your present objective. At the same time, characters that stop in squares adjacent to each other receive a defensive bonus. Jeanne has a sort of Fire Emblem-esque approach to damage, where characters can withstand four attacks if they're lucky. Thus, you have to strike a balance between rapidly advancing across the map and moving in formation, as the defensive bonus can make all the difference in the world.
The interesting thing about how Jeanne d'Arc treats the actual strategy involved is where it places the difficulty. In many maps, you're in little danger of getting wiped out by enemy attack. Instead, you're much more likely to get a game over by blowing your map objective, which is where all the challenge lies. For example, an early map requires you to save an NPC that's all the way on the other side of the battlefield. You've got roughly three turns before he dies, if you're lucky, so the question becomes how you're going to get to him in time while maintaining your own survivability.
This is the kind of gameplay decision that's hard to criticize. On the one hand, it's genuinely challenging in a way that a lot of strategy games really don't tend to be, and it actually does test your strategic acumen. On the other, it also means you're going to get whacked with a few cheap game overs. Whether this is a negative or positive is a matter of personal taste. On my end, I respect what it's doing, even if it makes me want to shotput my PSP.
The biggest problems Jeanne d'Arc has are, sadly, intrinsic to it being a PSP game. It spends a lot of time loading from the disc, so there's often a short delay between your pressing a button and the onscreen reaction. Playing a PSP game at all makes the damn thing sound and act like it's on the verge of crashing, and Jeanne d'Arc's already somewhat slow pace is made slower by the constant loading delays.
If Jeanne d'Arc was a PS2 game, it'd be one of the last great games on the system. As a PSP game, it's definitely a reason to own the system, although it has a surprising difficulty curve that may frustrate some players. Like every good game on the PSP, though, it also serves to highlight the system's flaws.