I like the DS for almost all the reasons already listed. I've got a shelf full of them. At least one of just about every kind.
I got my PSP free from a friend a while back. I have like four games for it. I was getting out of gaming when they were getting popular so I don't have much nostalgia for it. I don't have much nostalgia for Playstation in general for that matter, but I will say as an adult gamer I find it is a nice, cheap way to get into some series that I'll probably never play or collect for otherwise.
It has the added bonus, depending on which model you get, of playing some of the games on the TV with component cables. FF Tactics comes to mind.
Oh, one last thing, the PSP is easily hacked for homebrew, so it has some really neat uses in that regard if your in to emulation. I've got mine outputting over USB so I can plug in to just about any PC and use it as a controller and play the PSP on the PC monitor.