I like both consoles, particularly the PSP. The DS is great because of it's unique touchscreen. The PSP is great for it's amazing graphics/screen and multimedia capabilities. The homebrew options for both are great too. I wouldn't make a contest in this forum mainly because it is about *Nintendo*.
EDIT: About the games, the DS games are aimed more for younger children. Whereas the PSP games are for teen-adult compatability. But, that's only in my opinion. :D
Note: Notice how Nintendo is vibrantly underlined in a forum like this.