The piracy issue is very complicated. The PS1 was easier to pirate than the N64 and it won. The PS2 was fairly easy to pirate and it won (though Dreamcast was even easier to pirate. Xbox was probably about equal in ease of piracy. Gamecube was harder to pirate though). The Wii is also fairly easy to pirate and it won (X360 piracy is more complicated and risky. MS banhammer is going down hard. piracy is non-existant on PS3).
HOWEVER, I think it's fairly clear that piracy is hurting the PSP. Low software attach rates, third-party devs publically criticizing the PSP for being a piracy haven, etc. The DS is also a piracy haven but I think it wasn't as negatively impacted by piracy as the PSP because parents buy games for their children. The PSP demographic is older. If you are a adolescent gamer, chances are your parents aren't going to be buying you games like they do for children. So what does an adolescent gamer with limited income do? Hack his PSP with custom firmware, download a bunch of games through illicit means and play the pirated copies. I HAVE seen parents go on forums asking us where to get flash cards, how to use flash cards, etc. (pretty lolz worthy. Way to be a role model for your kids) but these parents are in the minority. Most parents don't want to bother going through all that trouble and they just buy the games for their kids. Especially when DS games are cheap (most start at $30, though some companies like Square-Enix arrogantly price them at $40). The type of DS gamer that is in the know about flash cards, firmware, etc. is most likely going to be an adolescent or adult gamer. This is probably why most of the "core" games on the DS don't sell very well compared to the big Nintendo IPs. Yeah the DS may have a boatload of jrpgs for eg. but how many of those jrpgs are good sellers? Most have underwhelming sales and I'm pretty sure piracy is a factor there because the type of gamer who likes those kind of games is more likely to be in the know.
The same goes for the Wii. The parents may be buying the games for their children but piracy is rampant among 'core' adolescent and adult Wii gamers.