I voted for both, but I bought just the PSP. I have always contemplated buying a DS, but it doesn't click to me. I could never get the hang of a system where i can only have one hand in order to hold the DS, and then expect not to drop it. I can't stand the Finger Strap Accessory, and yes I have used it, and even though the games can be fun and innovative, I really feel like I'm paying a hefty price for a mini game like Brain Age, or Pokemon Troze'.
As many faults as the DS has the PSP has some of it's own. A high price tag, and semi low battery life (When you play games as much as I do, which isn't long, you tend not to notice battery life.) Sometimes the game prices can be high, which makes you skeptical about what game you buy and so you tend to watch a lot of X-Play, starring two people who hate everything, but it rubs off on you and then you start hating those games without really giving them a chance, which is what Hollywood Video was invented for in the first place. That, and the machinery seems really fragile, so you tend to become a little frightened about carrying it around, but you get used to it after several months.
Both sides actually do have good games, if you take the time to actually PLAY them and don't listen to reviews. I have 8 PSP games so far in a list of more that I hope to get soon. I'm also sure the DS has games that are great too. Star Fox, New Mario, as well as others that I'm sure I'm forgetting. When you think about it both Nintendo and Sony were going at a rough start. Nintendo I think just got back on their feet faster than Sony, but Sony is coming along.
Just think about it real hard and decide for yourself. The handheld decision is a difficult one, and honestly you shouldn't really be asking others about what's right for YOU.
Meh...sorry for the probable grammar/spelling mistakes.