I don't think piracy had anything to do with it.
I like mai's idea. The PSP isn't different enough. The DS is.
The PSP is too similar to consoles (when you compare game libraries anyway), so it's basically a portable PlayStation, and its best-selling games is a GTA game that's also available on PS2. Turns out the consumers liked that a lot and it sold over 50 million, which is a great success.
It also turns out that more consumers preferred their handheld game library to be radically different from consoles and radically different from other handheld systems. So they flocked to the DS like nothing before, and the DS's best-selling games are exclusives that require exclusive controls, like Nintendogs and Brain Age.