I've played the PSP and the DS, DS Lite, DSi, DSi XL & 3DS. In comfort for holding, the PSP gets my vote here.
The screen's are about the same but the PSP has a lower refresh rate, but is more clear on the other hand.
The PSP has more processing power than the DS, hands down.
The DS has a better battery life than the PSP as well.
Now this is for the originals. If you're planning on getting the Vita then I do not know but I am 90% sure that the PSP Vita's specifications are miles ahead of any of the DS versions' specs.