Both are capable of fitting in your pocket and solving the 'I'm bored' problem. In that much at the very least, they are competing.
The PSP was sold on its functionality as a media player and internet device, two areas that Apple's touch devices perform very well in. So here again, there is competition.
Finally, there is some evidence that the iPhone/iPod Touch game market, at least in some regions, is claiming more revenue than the PSP game market. I take Flurry's analysis with a grain of salt, because they have a stake in the iPhone that they don't have in the PSP, but again, this looks like evidence enough to say the platforms are competing.
So why shouldn't we compare these two devices? Because one has a D-pad and the other has a touchscreen? Because one sometimes distributes games through retailers and the other never does?
The best argument I can think of is that an iPhone or iPod Touch can be enjoyed very much by a user without ever downloading a game for it, while you'd have to be bonkers to buy a PSP with no intention of gaming on it. The same can be said of PCs and home consoles, yet the PC game market and console game markets are constantly compared to each other.
"The worst part about these reviews is they are [subjective]--and their scores often depend on how drunk you got the media at a Street Fighter event." — Mona Hamilton, Capcom Senior VP of Marketing
*Image indefinitely borrowed from BrainBoxLtd without his consent.
