Well, no other handheld can compare with the PSP's graphics but those graphics come at a price. Sony has said that the batteries will last for 2-8 hours depending on the game; that 2 scares me and Sony's known for making their products seem better than they really are (such as the poly count for the PS2). Second, the PSP will be selling in Japan for the equivalent of $300+ US; that's way too much for the average person and I can't see them lowering the price much (if at all) in other regions. Third, it has moving parts, this is not good in a handheld; the Gameboy has always been able to take a beating and still work, that certainly won't be the case with the PSP. And lastly, they're going head to head with the Nintendo DS which may have worse graphics but it has 2 screens (one of which is a touch screen), wi-fi, a mic, 8-10 hours of battery life, $150 US, no moving parts, has a few months head start, and honestly, Nintendo's the king of handheld gaming.
Don't get me wrong, I hope Sony finds some success -- Nintendo needs some competition in the handheld market -- but I just don't see it happening. Sony's about to find out that they aren't as invincible in the gaming industry as they thought.