They're designed for two different things, as you said, but that means more then just what the box says. The PSP itself, running Linux, would not necessarily run Linux as well as the Zaurus, because the processor is designed specifically for gaming. Hardware wise, the Zaurus is much more expandable, as it has the CF and SD slots, whereas all the PSP has is a memory stick slot, which, to my knowledge, has no/few accessories. The Zaurus is much more expensive because of the software, not the hardware. It has an officially supported OS, with multiple accessories, and is designed for a wide variety of tasks. The PSP is much cheaper because it's designed for a single purpose. (relatively speaking)
Lastly, do some more reading on the PSP, and you'll discover that the PSP is actually worth a lot more then what it's sold for. Analysts say that Sony loses $150 US with each PSP sold, they make money on the games. [That's $150 US in profit, not $150 US in losses, they still make money on them, albeit only a bit] Both the Zaurus and the DS are sold at roughly what they are worth. Add in the $150 US, and the price difference evens out a touch.