The two handheld consoles are really very different from each other.
The PSP has a very bright and vivid wide screen display that is just gorgeous. It has graphics similar to that of a Playstation 2 and has a great library of games. Most games are action oriented (3rd person shooters, 3D platformers, fighting games, and a few FPS games.) The PSP can also play special UMD movie discs of which there are many titles to choose from. Additionally, the PSP can be used to surf the internet over wireless internet and it can also allow you to view pictures, play music, and watch videos which you would store on a meory stick pro duo stick.
the DS is a cool console as well, though it's definitely not suited towards everyone. Its big highlight is the touch screen interface and the fact that it has 2 screens. The graphics are much less then the PSP and can be compared to the Nintendo64. The game selection is often more focused on games for younger people and you won't find very many adult oriented games like you would on the PSP.
To help you make your decision easier I recommend reading several reviews on each product. For a ton of good information check out the wikipedia articles on each one.
PSP:
http://en.wikipedia.org/wiki/PlayStation_Portable
DS:
http://en.wikipedia.org/wiki/Nintendo_DS
Hope this helps you :)