sI had a DS and thought it was ok. I am not really into mini games, so I got bored of it. I tried the some of the more in depth games, but it just wan't for me. The only games I enjoyed on it, were the platformers. Before I sold it, I was playing it about once a month. I bought a PSP on a whim four months ago. I rarely go a day withought playing it. The platformers I have played (R&C, Daxter) I have enjoyed way more than the ones on the DS. I have also enjoyed games like Tomb Raider, Killzone, and Syphon Filter, MLB08, Pro-Evo, which wouldn't be possible on the DS. Obviously there are just as many games for the DS, which because of their control scheme wouldn't work on the DS, but very few that I enjoyed. y\Yeah the DS has more titles, but the DS has a very high percentage of shovelware, like Horsez, Barbie gets Boned, etc.
Good range of RPG's, strategy games, etc. I also love the multimedia capabilities of it. If you have a PS3, the remote play is awesome both for gaming, and watching videos.
My biggest knock on the PSP prior to owning one, was that most of the games on the system, are console type games, so why wouldn't I just play those games on a console. For a portable I want pick up and play, and a game with too much depth is not good for pick up. Turns out I became bored easily of the pick and play type games of the DS. And being short of time to play console games the PSP fills in nicely. Sony forces devs to implement sleep properly, so you can put it to sleep in the middle of a boss battle, and pick it up a month later and keep playing. Nintendo does not require devs to fully implement sleep, so as a result, most games just shut off the screen, and pause the game when you close the DS. So it is still burning battery.
You should borrow a PSP for a week, with a game or two that you are interested in, and see what you think. Because it really comes down to the style of games you like. That is what it was for me. (Unfortunately I bought a DS in the process of figuring out my answer.)
~S