The DS :
1) has a touch screen that allows for more interactive gameplay;
2) smaller in size;
3) is easier to 'hack'. It's not really a hack since you never do anything to the DS itself. It just requires a flash kart to play homebrew, roms, etc;
4) is slightly cheaper;
5) uses flash karts that takes microSD which are very much cheaper than MS;
6) has much smaller rom size therefore 1G or 2G of memory card is enough and much faster to download;
7) does not have good graphic display as compared to PSP;
8) requires homebrew apps to do many other things like watching movies, listening to music, etc(not sure how movies will turn out with dual screens though, never tried);
The PSP :
1) has great graphics compared to the DS;
2) has games that are more serious games like God of War, SOCOM, etc;
3) allows you to watch movies, listen to music, etc with relative ease;
4) is more difficult to mod;
5) requires memory sticks that are most costly;
I really like both actually even though I just got my PSP(that explains the shorter list). The DS is more fun in terms of interaction with the touch screen and the PSP has games with better graphics and closer to the PS3 and Xbox360 games.
