Here is my opinion of both systems. I've owned a PSP since launch day, own 2 DSs (one since launch day), and just bought a import DS Lite 3 weeks ago. I brokedown each system by category, since each system has it's fair share of ups & downs.
Value:
PSP: Costs $200 (only because the $250 bundle is not worth it if you you want to use it to it’s full potential), then you have to buy a memory stick (512 MB runs $40-$50, IGB runs $50-$70) and a protective case (I suggest the Playgear pocket at $20). The games generally run about $40-$50 and the UMDs are $20-$30.
DS lite: Will cost $130, you do not have to buy a memory stick or a protective case (since the system folds down to protect the screens)...but for argument sake most DS lite cases would be about $10-$15. The games run about $30-$35 and it does not playback movies....but it does have the huge library of the GBA (which most of those titles are under $20).
Winner: DS Lite
Graphics:
PSP: This is a no-brainer. You basically have a PS2 in your hand. Although some games look like crap, most of them look really great!
DS Lite: Graphics are not that bad. This is still a gorgeous system...but they are still N64 -Dreamcast style graphics.
Winner: PSP
Handheld features:
PSP: Let’s face it. Handhelds are different than console systems and should be judged as such. For example: Loading times, which is what the PSP seriously suffers from. Do you really wanna be on the john & spend most of your time looking at a loading screen....or how about taking a short car ride to the local store and have to stare at that loading screen for most of the trip? You have to realize that there is alot of loading when you own a PSP. Some positive handheld features (that the DS can’t touch) is the built in MP3 player, photo album, and movie right off the memory stick...hence no load times. Those few features have come in handy pretty often for me. Yet another handheld feature is it’s portability. PSP is one of the bulkiest handheld ever made (behind the Sega Nomad and Atari Lynx) and it’s battery life is alot shorter than the DS Lite.
DS Lite: DS has it’s fair share of load times, but not near as long as the PSP. DS Lite (like I said earlier) does not have MP3 playback, photo album, or any of those other feature that the PSP has. The portability of the DS Lite blows the PSP out of the water. It is a very portable system (that easily fits into your pocket) and has a lengthy battery life.
Winner: DS Lite
Controls & Gameplay:
PSP: Yes, they they on an analog nub that the DS does not have...but I find it to be cumbersome in most games. There a few games that use the analog nub in a way that is feels smooth. The D-Pad also feels a little more stiff than the DS Lite. The buttons themself feel just as responsive as the DS Lite. The L & R buttons (or triggers) actually feel better than the DS by a margin.
DS Lite: The D-Pad has to be the most responsive D-Pad on any handheld. It makes racing games, fighting games, etc. smoother than playing them on a standard DS and the PSP. The stylus is used intelligently in most of it’s games. It brings a fresh-new feeling to games that come out for the DS.
Winner: DS Lite
Game Library:
PSP: Has a decent about of games, for being out for little more than a year. The game are the same games you’ve played on your PS2, Xbox, DC, GC. Which is not necessary a bad thing. A large amount of people want to play the same game on their handheld as they have on their PS2. There is a market out there for these games, it’s just not for me. If you are into FPS, sports titles, racing, etc. games... then the PSP is perfect for you.
DS: Has about a dozen more games than the PSP.... but it also has the 1000+ game library of the GBA. I feel the novelty of the DS games brings something new to the handheld market. I find those games more interesting. So if you like novelty games (Nintendogs, Animal Crossing, Brain Age, Trauma Center, Phoenix Wright, Meteos) then this is the handheld for you.
Winner: Draw
Bottom Line: DS Lite is the best investment, has the best handheld features, and has just as good as games as the PSP (better IMO). It just doesn’t have as good graphics...does that really matter if the games rock? I’d say go with the DS Lite until the PSP price drops & you can get a 2 GB stick for about $50.