I have more than one of both.
The answer will definitely depend on what kind of games you like.
If you want to play scaled down console games, go PSP.
If you want to play games really intended for the mobile gamer, go DS.
I love both and play both often. The DS is better for me personally, just due to the fact it has more games I like (I love Castlevania and a few other old-school style games).
The DS is definitely the safer buy right now. The PSP "2" should be coming out in a year or less.
One more thing to consider is that the PSP is a full on PMP. A serviceable MP3 player and video player ready to go, with a....well...less than stellar web browser, but if your phone doesn't have one, it can do the job in wifi locations.
But I suppose the catch is that the main reason that console-esque games (in general) don't get brought to handhelds is because they just don't play well in the mobile environment. Mobile gamers often have short play sessions, often as short as 5 minutes at a given time, so it's helpful to have a library of games that can be picked up and put back down again without losing your place. With the DS, you simply close the lid and it automatically goes to sleep with your place frozen safely. When you're ready again, just open it up, and there's no load time or anything, you're exactly where you left off. The PSP is similar, with a switch on the side, but you'll probably want to put it in some sort of protective case to take care of its screen, the on/off (out of sleep) isn't as fast, and in between levels (Etc) there are short load times, all of which chip away just a little bit at its capacity as a purely mobile game system.