I don't have a PSP, but feel free to read my gripes with the DS;
The Nintendo DS is great for a quick 10 minute play if you don't have many other options at that moment. However, it's selection of games is limited, with 3/4 fitting into the "seriously lame" category. Its graphics capabilities are poor at best, dwarfed by primitive consoles such as SNES (in my opinion). Its supposed to be the next step up from a gameboy, but even then I feel it lacks the same charm. The game cartridges are also the size of a camera card...which is odd given most of the games look to be designed for toddlers who would swallow the damn things.
The area the DS excels in is puzzle games, which are arguably one of the few reasons this console has ever sold.
If you want a pocket games console, the PSP looks to be the only option of late.
If you want an electronic puzzle-book with Brain Training games, choose the DS...or better still, save upto ?80 by buying a puzzle book instead!
(please note, this review is written by a Carlos who loved Pokemon Red, Yellow and Gold, but then grew out of them. This reviewer has also never understood the appeal of Final Fantasy)