There's nothing wrong with iPods. They're just as reliable, if not more reliable than other MP3 players. Everyone keeps complaining about how they always break and die out. For every Pod that meets misfortune, there's another 50 that work perfectly fine for years. I've found this true for many other mp3 players like Zen, Dell DJ, and yes, Toshiba. What really makes iPods so great against other mp3 players is the numerous accessories available for them. If you're into that kind of thing, get the iPod. Plus, used and refurbished Pods are much more readily available on eBay than other brands. Just don't let people try to convince you that iPods suck balls, because the same could be said in comparison for every other mp3 player on the market.
Now to the PSP. I would say no. That's a personal preference though. Since you are choosing between that and the iPod, I'm guessing you're interested very much in listening to music. The PSP isn't built for that. You need to buy memory sticks for it, which cost close to a stand-alone mp3 player. The games are geared mostly towards racing and sports games, so if you like those, the PSP isn't a bad choice. Plus there's always emulators.
But, overall, I'd say get the iPod. People may say that they're terrible, maybe because they knew someone whose iPod broke and automatically made severe judgments about it. Or maybe because they're just Microsoft fanboys who can't stand anything Apple. But they're not a bad product by any means, and I'm looking into getting a Mini myself.