The only reason I'd get a PSP would be for homebrew functionality.
and if "firmware", "homebrew" and "downgrade" are terms you're unfamiliar with, go for a DS. You won't regret it.
So you don't think it depends on what kind of games the member enjoys?
well. I think the only thing that PSP does (in a gaming sense) that the DS doesn't is better graphics.
any game style on the PSP can be got on the DS, but the DS has a broader range anyway.
So IMO, unless you want to get your hands 'dirty' with homebrew then the PSP isn't worth the pricetag
I would get the DS. It has the games and it's intuitive. Plus, you get twice the gameplay screens

Also, you might want to consider making this a poll.
Wow, I thought the PSP was considered dead since the DSL came out and kind of rocketed off in sales. Either way, I heart my DS and DSL, and I can actually find other people with them in airports and waiting rooms, which is nice for a quick local multiplayer game. (not to mention that between me and my immediate family, we have 6 DS's, which means some crazy multiplayer action when I go visit).
ds cause its fun, online, kool, you can interact with people, and the stylus is always fun to use
and mario
well. I think the only thing that PSP does (in a gaming sense) that the DS doesn't is better graphics.
any game style on the PSP can be got on the DS, but the DS has a broader range anyway.
So IMO, unless you want to get your hands 'dirty' with homebrew then the PSP isn't worth the pricetag
Even if homebrew was in question, I would still say DS. It has much better homebrew than PSP does and you can use NDS homebrew without doing anything that could brick it or void your warranty. All you need is R4DS (or something similar), and a memory card, together they cost about the price of a new NDS game.
you've pretty much heard it here several times
DS = wider library of mostly more entertaining games, no long loading screens, simpler multimedia with the R4 and less risk of utterly screwing up the system
PSP = a few more "hardcore" titles
i really can't say the PSP has better graphics, because i think a game like Children of Mana with its vibrant colors and fantasy filled world looks better than a bunch of blocky character models in some of the half assed PSP titles
The DS is cheaper as well, which means more money for games.
you've pretty much heard it here several times
DS = wider library of mostly more entertaining games, no long loading screens, simpler multimedia with the R4 and less risk of utterly screwing up the system
PSP = a few more "hardcore" titles
i really can't say the PSP has better graphics, because i think a game like Children of Mana with its vibrant colors and fantasy filled world looks better than a bunch of blocky character models in some of the half assed PSP titles
Well put.
I would go with the DS purely based on its library of quality titles because you can get media from another device.
Games people make and can be downloaded..I Think.
PSP FTW better graphics god of war gta MGS ratchet and clank is fun plus connects to PS3
Metroid, Mario, Pokemon, Zelda > God of War, GTA, MGS and Ratchet and Clank.
DS touch screen > PSP graphics.
nah god of war is the best game ever created

well, as i can see DS seems to be the popular choice....... but! this is a nintendo site. So there are of course many fans of the DS? But, i really do enjoy the ps2 titles, infact im in love with my ps2 =] (and my wii

)
And then agian, psp has music, and picture& all that, but i do have my ipod!?!
I DONT KNOW! THIS is so hard........ still don't know.. but so far i'm going towards the side of the PSP =S
dang, i sound like a sony fan?
and um, i like mature titles

yeah mature titles FTW 
hehe How cool is Halo, Who is obsessed with every other console but the wii

yeah but i have and play the wii a little

I have both and I think the better buy would be the DS Lite.
Basically depends whether you'd use the PSP 'legally' or not

if so, get a DS, if not, get a PSP ;D