Nintendo DS is better than a PSP for gamers. The reason is simple really, the NDS offers developers much more game-space due to its unique hardware combination of dual screens and a random access control in the form of a touch screen.
Let me explain what I mean by game-space: fundamentally any human-computer interaction is limited by the interface available to the user. In this regard the PSP offers very traditional combination of interfaces - a few buttons, an analogue joy stick and a microphone. This means that games for the PSP will have to work with these limitations, the corollary of which is that developers will only have so much room to work with when it comes to making games. Thus the range of games possible on the PSP is restricted by its controls, and this is what I mean by game-space.
The NDS on the other hand expands the traditional console game-space significantly by introducing not only an extra screen but also a random access control in terms of a touch screen. A random access control is one where there is no analogue movement from point A to point B such as that seen when controlling a cursor with a joystick for example. The advantage of this should be immediate to any PC gamer - its the console version of a mouse. Many games require the use of a random access control to be enjoyable, most noticeably first person shooters and real time strategy games.
Whilst the PSP can do some pretty funky things out of the box, like play UMD video, NDS offers gamers the chance to play games that well, has never been seen before while PSP will offer the same formula of games over and over because it can never be free of the shackles of its limited controls. Those games might be great, but they won't be new and great - there is only so much you can do with buttons and joysticks!
Now if the next iteration of NDS came with motion sensors, then boy are we talking whole new realm of gaming experience!