The PSP & DS are completely different machines aimed at different markets so imo there's not much point comparing them.
The PSP can handle far more impressive graphics than the DS, its roughly like a lower res PS2. The games available for it are similar to PS2 games, and it will have a lot of conversions of these 'Proper' / 'serious' games. However, we aren't going to see any surprises.
With the DS Nintendo are trying to do something different. It didn't want to be a portable gamecube, they said from the start they wanted something different, that could offer playing experiences that people couldn't have with home consoles, hense their experiements recently with controlling the games through touch, voice, light and movement, not to mention the extra possibilities cause by having two screens.
For my money, the DS hasn't done anything so revoultionary to make me stand up and go 'wow' thats different AND BETTER. Unfortunately weird control systems are in my opinion faddy and short lived. I've seen Bongos, Dancemats, Fishing Rods, Eyetoy, and all kinds of other control methods come and go, and none of them are going to go down in history as changing gaming for good. However I'm all for originality and if Nintendo want to experiement till they find something worth using, thats fine by me. As soon as they find something worth sticking with, Sony will follow suit anyway - Nintendo were the first company to popularise Analogue Control, Vibrating force feedback pads, and in earlier generations did the same with memory cards, light guns, shoulder buttons and dpads. All of which people criticised at the time.
Nintendo are experimenting, and it may well be a failed experiemnt in the long run, we'll have to wait and see. But as far as I can see the PSP is nothing but a portable PS2 (hense the name) and personally I don't feel the long play times of GTA or the hyper sensitive controls of wipEout are suitable for a quick ten minute bus ride, and are much more suited to playing at home. Not exactly portable games, the most sucessful portable games are easily understandable, simple to pick up and put down when needed, and not requiring 100% of your attention (Don't want to miss the bus, or get run over in the street!)
Of course in the technical and conventional sense of the word, the PSP is capabale of far better games. I'm just not sure thats the best idea for a portable system, and would rather they concentrated on releasing some real AAA titles for PS3 instead, and not have a repeat of the PS2s initial launch (It was only when GT3 was released that I bought one, and not till GTA3 that I recommmended others did!)
Unfortunately it is an ill informed idea that only the PSP can play films, music files, pictures etc, the DS is more than capable of doing so from the off, as were the GBA & SP, there are plenty of official and unofficial spericals to choose from that use flash memory in a startad size GBA cartridge on which you can put whatever you wish.
Also in america you can buy many 'videocartridges' for the GBA / DS including mostly kids and teen shows such as Spongebob Squarepants episodes or Hilary Duff music videos, equally as pointless and overpriced as Sonys UMD movies
I don't think its wise to compare the DS and PSP at all, both entirely different beasts which play very different games neither of which would owrk on the other. TRy releasing Nintendogs or Warioware touched on the PSP? Wouldn't work. [sarcastic voice] And a decent Ridge Racer on the DS is so technically impossible that they wouldn't even bother trying. [/sarcastic voice] Oh wait, they did, and it was awful.