The DS has sold more than the PSP:
DS: ~70 Million
PSP: ~55 Million
The DS has two screens, one is a touchscreen
The PSP has a much higher resolution on it's screen (and higher in PSP-3000)
The DS is cheaper than the PSP, and has better battery life.
The PSP has much more quality and performance than the DS
The DS needs apps or games to use the internet (DSi has internet built-in though)
The PSP has built in internet functions
The DS has a few features with Pokemon and the Nintendo channel
The PSP can be used as a PlayStation 3 Controller when connected
The DS has quicker loading times
The PSP has a memory card slot (however, the DSi has an SD card slot)
The DS 'closes' so it can't break as easily, and is easier to carry
The PSP has better controls (analog, digital)
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Yes, it can since the Nintendo DS lite is slightly smaller than the original DS
A Nintendo ds lite costs £100
Nintendo invented the Nintendo DS and the Nintendo DS lite.
Yes, the original Nintendo DS as well as the Nintendo DS lite can play NDSi games.
There is no such thing as a 'DS lite' game. If it's a Nintendo DS game, it works on any model.