I don't know what is about the NDS (and N-handhelds in general), but the games have never really held my interest for long. The exceptions to this were Mario Golf and Mario Tennis. Other than those 2, I just really can't get into the Nintendo handhelds. The screens are too small, the sound is awful, the graphics are outdated (it's 3D is a joke), and the control is carpal tunnel inducing even if you use the stylus. On the plus side, the DS is so simple to hack, that even a caveman could do it. The games are small enough that you can fit 100-150 of the latest ones on a 4.7gig DVD-R. There are tons of games still coming out for it. The storage media (micro-sd) is much cheaper than Mem-stick, and you can fit a lot more games on a smaller card.
I have to admit, I've played my PSP more in the few months I've had it, than I have the DS I've had for a year and a half. Partly because I love driving/racing games, and the analog nub rules for that. The graphics are far superior, and the buttons feel much more sturdy and responsive. The games are what they are...I haven't played a bad one, they just aren't making that many for it any more. Another thing is that the PSP comes with the features built in that the DS doesn't. Multimedia. Movies, music, pictures playing capability built right in. A perfect PS1 emulator (thanks Sony!), wallpaper and theme support, Wifi, USB and memcard slots, digital camera syncing, and FIRMWARE UPDATES.
That being said, it's a little more expensive to get started, the system itself, and if you want to hack it I recommend getting a premade Pandora and magic memstick (about 30-40 dollars). 4gb memsticks are 30-55 dollars, and a 2gb is really the minimum you need because the largest of the games are 1.6-1.9gb. If you're just getting started there are plenty of games to play, but the future looks kind of bleak...there ain't much coming down the pike in the way of games, let alone really great ones.