I'd have to call it a tie here. The NDS has some pretty damn cool features, the mic, the touch screen... Well alright, the mic is pretty lame, but the touch screen is damn cool, and I've seen it used pretty well (I <3 Kirby). The DS also has the ol' Nintendo lineup going for it, Mario, Metroid, Zelda, you know. Also has the damn fine backwards compatability, so I can play GBA games. And it also has Castlevania: Dawn of Sorrow, which I've heard is damn near as cool as SOTN.
The PSP on the other hand only ties since it recently happened to get Valkyrie Profile on it. I mean, it has too much stuff on it, and it's very expensive. It's more powerful, and half the games show it, it also has the capability for a more advanced control system (with buttons, the touch screen is in a whole other league). It even functions as a music/movie/picture viewer, and can fit a whole bunch of stuff on it (assuming you want to shell out $200+ for a 4GB memory card), so I can listen to random music, read some comics I uploaded on there (not that it's easy, the bloody screen requires you zoom in incredibly far to read), and maybe watch an episode of Aqua Teen Hunger force.
Now we get down to homebrew and stuff like that. Most would instantly jump for the PSP in this department, since if you get your hands on a so called 'golden 1.5', you can pretty much emulate any system short of the N64 and PS1 (the PS1 is apparently going to be emulated by Sony, wee!) pretty well. The GBA emulation kind of sucks since the games are pretty advanced, so you'd have to stick to slow paced ones like Advance Wars. The SNES and Genesis emulation is excellent though.
But on the other hand, the Nintendo DS can pretty easily just get a flash cart, and you can load a lot of stuff on there as well. I haven't experimented with this quite yet, since I haven't had a DS for long and thus don't have a flash reader. I can't say much, but I doubt the DS is far behind the PSP in terms of this sort of stuff.