The PSP didn't really work out as planned for Sony. It was designed to weaken Nintendo's commanding grasp on the handheld gaming space, but it ended up falling well short of those goals due to a number of problems. The most glaring of those problems was software support. While the PSP saw plenty of shoddy ports of console games, the great titles were few and far between. In recent years, just one or two must-play titles would come to the PSP a year, hastening its obsolescence.
Which begs the question, why would Sony even bother trying this again? Well, for one thing, they're Sony. And for another, they think the NGP (Next Generation Portable, a temporary name) is the way of the future. Having spent a couple of hours playing through a number of the NGP's games, it's clear that Sony's got another technological marvel on their hands. But are amazing graphics enough to convince the world that they need to carry another gaming device ever day? That's a harder question to answer.