My wife and I each have both a DS and a PSP and that is the perfect solution because they're both excellent systems. But if you must choose just one, this is what you need to do. It is the most practical way to choose any game system.
Go to a store where they sell these and look at the games available for each. (You can do this online as well.) You will notice that the DS has games more suitable for younger players like the Mario-style games, you know...cutesy games. This is not a bad thing because they are excellent games! But PSP has games more suited for more mature players such as Grand theft Auto, Metal Of Honor, etc. The graphics on the DS is perfectly suited for the games it plays, but not quite as advanced as the graphics on the PSP. There is one big point in favor of the DS though....
There are more games available for 2 players using a single cartridge than there is for the PSP (using a single disk) which I feel is a BIG mistake on Sony's part. For instance, my wife and I can play each other on the DS playing Bomberman using a single cartridge wirelessly, but to play Super Puzzle Fighter wirelessly on the PSP I had to buy the game TWICE! (A disk for my wife and one for me.) So, as you can see, Nintendo is much more generous which will save you a ton of money if you expect to be using your system for wireless 2-player games. I liked the DS so much that I even bought an extra one!!!! Why? Because the Clubhouse Games cartridge has a wireless 2-player chess game on it and I can hand one DS to a friend at work and although he works in a different department, we play wireless chess all day! SWEET!!!!
Now, one nice thing about the PSP that the DS doesn't have is the ability to play your favorite movies in the palm of your hand. That's kinda neat if you'll be doing a lot of that kind of thing. It's not a big deal if you won't be watching movies that much. (You buy a $30 software thingy that copies and converts your favorite DVD to PSP format - works good for home movies recorded on DVD as well!)
So, the bottom line is, you need to look at the type of games available for each system and decide which games you'll want to be playing.
There you go! I hope this helps. Good luck!