I've said this a few times already, but when Nintendo is pegged as a front runner, history shows they've done bad. If Sony has a successor to the PSP to announce, given the kind of third party push Sony has (so much so to reignite interest in a handheld that's ship already sailed, and a push that stole third parties from Nintendo in the 90's), and their ability to create a network, there is no good reason to count them out. The GameCube doing what it did didn't hurt the Wii, the same should go for the next PSP. Many see this wave of AAA PSP titles (MGS, KH, God of War, Resident Evil, etc.) as Sony's way to allow the platform to die with the public's good faith.
Apple on the otherhand isn't a real compeitition. They've created a market where games like Metal Gear Solid 5, Kingdom Hearts: Birth By Sleep, and such wouldn't be able to be made simply because that market wants $1-$10 games, and those types of games won't make their budget back with that price. It's a problem that Apple has yet to see any reason to fix, which is to be expected, as they've never released a game themselves, and thus haven't seen the problems they have done. Not to mention the fact that with Apple, it's incredibly easy to get a dev kit, it's just that once you have it, don't expect any sort of support at all from Apple. Which is why we've seen so many independant studios who started out making iPhone/iPod Touch games jump ship to DSiWare, WiiWare, PlayStation Network (normal releases and Minis), Xbox Live Arcade (normal releases and Indie Games), and even Steam. The Apple platforms are very much cellphone games, cheap and forgettable, no one buys a cellphone to play games on them, and no one buys Apple's devices to do the same either. You'd have a hard time saying that in regards to Nintendo and the PlayStation line.
Notice how I didn't even have to rule out the fact the Apple platforms are insane with their idea of no buttons to discredit their place in the market, hahaha.
The hurdle for Sony is putting on a good example for everyone else to see. Sony in North America and in Europe gave up on the PSP once in the lead up to the PS3 launch, incidentally, that's also when the DS took off and erased the lead the PSP had created in unit sales (if you don't believe me, early on in the DS's life, Nintendo had the NPD group combine the GBA and DS sales together because the DS was performing so poorly). They've admited they ignored the platform because the PS3 was costing the company billions, so hopefully they have the ability to keep things together this time around, because a handheld market with only 1 real player, isn't really a market and it doesn't strive anyone to innovation.