I have both systems, got the PSP over a year ago and the NDSL last week. I even have games that run on both systems....here's the breakdown::
PSP
+Much better graphics. Lots of bling...
+Has more sports games available (like EASports series). Madden on psp kicks the snot out of the NDS one. A couple gen difference.
+More flexible as a system (browser, music, pix, videos). More refined OS.
+Feels better in the hand, less tiring than NDS (imo)
-Slow loading times , very slow at times.
-Shorter battery life
-Not enough original games - mostly ports from PS2 or whatever. And too many compilations.
NDS
+Dual screens. Touchpad gaming....new experience.
+Instant loading in games
+More "must-have" games and original games. Like New SMB, mario kart, trace memory, trauma center, etc etc...
+Excellent battery life
-Touchpad sometimes integrated into games for no reason. Other than the fact that they can...it is painful to play Resident Evil with buttons and then all of a sudden pull out a stylus to hack away at a monster....um
-LOTS of "cartoony games" based on anime stuff. perhaps it is more limited on graphics...
-NDS buttons are small, my hands cramp up and the new lite case feels like it'll slip out due to its glossy nature
IMO, both systems haven't reached its potential. PSP games thus far have been mostly rehashes from PS2 or compilations of games of yester-year. But the gameplay CAN be equal of the NDS due to the analog stick...just that they haven't come up with many GREAT games yet (mostly eye candy games). I am guessing the development time on the psp is substantial. However I also use my psp as a quick browser and especially a movie player on the plane. It is more flexible, does many things well, but nothing great.
NDS on the otherhand, has lacking gfx and sound...but the games have generally sucked me in. New Super Mario Bros maybe 15 years old in idea, but very very fun to play to this date. I'd like to think that developers know there's a handicap on graphics and spent more time on the depth of the game. Lastly, opera is coming to NDS sometime - and it'll be more natural with the stylus.
Look at what games appeal to you. They both have good games. I like action and sports games (madden, nba, socom) but also like classic nintendo ones too (mario, castlevania)....
My advice, if you can afford it, get both. If the psp is the swiss army knife, the nds is the best steak knife you'll find.