I don't see how anyone can say the PSP has no games, that seems to be a trend lately. I have THUG 2 Remix, Wipeout Pure, Death Jr., Lumines, and I'm about to own Burnout. They all kick major ass. I plan on getting GTA, WWE Smackdown vs Raw 2006, and Infected.
To be honest, if you're looking for a handheld for 100% straight gameplay, get a DS, nothing can ever match Nintendo's first party games. If you're looking for a handheld with great gameplay but with focus on other features like, mp3 playback, UMD movies, homebrew video, pictures, and a big ass bright screen... get a PSP.
For me, my DS is nice for around the house. It's not good for a car trip, or outside play. The screens aren't bright enough, and the touch screen thing doesn't working well on a bumpy car ride. The PSP I like to break out on my monthly drives to Vegas, and when I need to zone out for extended period of time.
For some reason stylus based gameplay always gets old to me fast. Kirby: Canvas Curse, Yoshi: Touch & Go, Nintendogs, and Warioware: Touched all got old fast. I still can play regular Kirby platformers, Yoshi's Island, and both Warioware's from the GBA forever without them getting old, but when the gameplay is solely based around the stylus they just get boring for some reason. I haven't checked out Advance Wars DS yet though, so who knows.