I think that the Nintendo DS is a far better system than the PSP.
My major gripe with the PSP is that it is an over-engineered piece of hardware that can't decide what it wants to be. Is it a game system or a media player? Sure, it
can do both, but I don't think it's necessary and it is hard to do both well. I have an iPod for listening to music on the go, and it is more portable than a PSP and has a better interface for playing music. I don't see the appeal in watching movies on such a tiny screen (that goes for the iPod as well as the PSP), especially when it meant paying $30 for a movie that I probably already own on DVD and can't use with any other device.
The PSP is a portable/handheld unit, but the games are generally designed no differently than games on the Playstation2 (or other home console). It's the same gameplay experience as playing on a home console, except you get cramped controls and a 3.5" screen to look at. Many of the games take a long time to load due to the UMD media format. Some games take 3-4 minutes before you're actually playing anything. If what you really want is the cinematic home game console experience (complete with loading times) shrunk down to a tiny screen, then I guess the PSP might be appealing. Plus the battery life is notoriously poor on the PSP (especially if the game accesses the disc drive frequently).
The Nintendo DS, on the other hand, was designed specifically to be a portable gaming console, and it doesn't pretend to be anything else. Its processing power and level of graphical quality is a little better than the Nintendo 64 console (but significantly less than the Gamecube), whereas the PSP's processing power is very close to that of the Playstation2. The tradeoff is that the PSP will often get about 4-8 hours of gameplay time from a fully charged battery, whereas I pretty consistently get a good 15-16 hours or more from a fully-charged DS. There is no fan noise or disc drive grinding with the DS and it generates a negligible amount of heat.
With every single DS game that I own, I can be actually playing the game within 30 seconds from a cold power-on. Resuming from standby takes 1-2 seconds.
To me, a portable game console isn't just something that I take with me so that I can sit and play a game for 3-4 hours straight wherever I feel like it. There are certainly times when I do that. However, a truly portable system needs to be one in which you can have an enjoyable gaming experience in play sessions as short as 5 or 10 minutes. Whether it's on public transit, waiting in the doctor's office, stuck in a long lineup at the store, I can pop open my DS, resume playing where I left off (whether it was suspended or powered off) and then put it away when I need to.
My point is that the DS was designed to deliver a different gaming experience than playing on a home console -- an experience that includes short bursts of gaming-on-the-go. The PSP was designed to replicate the home gaming experience in a handheld form, and I think that was a mistake on Sony's part.
When you compare the game libraries between the DS and the PSP, you can see these design goals reflected. The DS library does include games that play very similarly to home console titles, but there is a much wider variety of gameplay experiences available on the DS than there is on the PSP.
And I haven't even mentioned the DS touch screen yet. I adore using the touch screen to interact with (most) games, and generally find it a much more approachable and intuitive interface than the traditional D-pad and buttons. It's not a good fit for some traditional styles of games, but it offers most of the benefits of a mouse and I find it often brings a more personal sense of involvement when I'm not just moving a pointer around the screen but I'm actually "touching" objects in the game world to interact with them.
There are certainly some good games on the PSP, but there are a lot more mediocre ones and even the best ones strike me as games I'd rather play on the 52" TV at home with a comfortable controller.
I ended up having to buy a 2nd DS Lite to give to my wife so that I could have mine back.
We're both really looking forward to Civilization on the DS, so I'm probably going to grab two copies on launch day so we can play together.