Somehow in my opinion, i would prefer PSP over NDS. Simply because psp has more quality games than NDS. I had to admit that NDS has many fun games such as pokemon but interms of quality i guess this is what NDS is lacking.
I bought the psp for myself and always telling my mum to get a NDS although initially she herself wanted a psp as i thought that it is more suitable for a person at her age plus i will be getting the chance to try out the NDS.
And my verdict is PSP is BETTER! Being a Final fantasy fan, i felt FF4 is too overated and i quit playing the game after a mere 40 minutes. Another game not worth mentioning is FF12 Revenant Wings, that game is a piece of crap. It seems that game developers are juz making games for the DS mainly is to make money and neglect quality for the game. Example of poor quality games, Call of Duty 4(wat on earth??? Why is this game ported into the DS?Obviously juz to milk some money),the Crappy Ironman for all the console(but the DS version is the crappiest interms of gameplay not graphic), Star wars force unleashed. Many of these titles does not have to come to a point where it suffers from quality in the hands of the DS. DS have quantity of fun games but more shitty games.
But i do enjoy several titles such as Phoenix Wright Attorney at Law(My all-time favourite),Pokemon,Digimon Championship,some Brain age and World ends with you.
For the PSP, i felt that it could have done better if it could gain support from game developers. It has so much potential but it is a shame it is being neglected by both the public and developers. The only thing that could make me hate the psp is the lack of games!!!

On the hardware area, credits must be given to DS for the touchscreen, inbuilt microphone and Online play via Wi-fi. But i kinda felt the concoles itself is using cheap plastic, it kinda felt like those kind of plastic chairs in secondary school. It doesnt felt comfortable pressing on it. I would not take graphics into account but the sound system is kinda poor, poor video output.
For PSP, nice holding it, wide screen, nice sound system, good video output( unless you are under the sun then it is terrible). Poor online play in which it does not have any game featuring online play(requires Xlink kai)
Overall i really do feel the PSP has an edge over the DS interms of gaming quality and hardware quality but trails behind DS interms of innovation and creativity.(I wont be comparing watching movies,music, or webbrowsing as DS does not has a direct features)