Which one is a better buy?

Personally, I'd take the Nintendo DSi. The touch screen opens up a whole range of possibilites for gameplay, and the new addition of the camera should be useful in the future as well.

Most importantly, though, I think that the DS platform has the widest range of fun and high-quality games of the three. And it's that that determines 'the best', no?

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My suggestion is the PSP if you are over 12 years old and looking for more "mature" games. I dont mean mature in, "mature" as in rating, I mean it in better quuality games, better graphs, and so on. The NDS is for little kids(and that i know from expirience) and the PSP is for more adult or mature kids, or teenagers, or whatever.