From someone who has both, here is my opinion:
Nintendo DS Lite:
+Cheaper (the system as well as games)
+Games are more original
+Longer battery life
+Quality first party games
+Great games coming out soon.
-No WPA support
PSP:
+Good games out in the future (Valkyrie Profile: Lenneth a Square-Enix RPG, sequel to Ghouls and Ghosts, FF VII Crisis Core, new Rockstar games, Lumines II)
+Versatile as hell (watch movies, music player)
+Homebrew/emulation community is more mature (NES, SNES, MAME, you name it)
+Beautiful screen, wide screen is great
+WPA support!
+Web browser built in out of the box.
+Sony constantly updates firmware with new features (but this would prevent you from emulation and homebrew).
+Graphics blow away DS, no comparison.
-Expensive (memory stick and system)
-A lot of games are PS port.
At this stage, I would get the DS Lite. It is fun little system, and PSP is collecting some dust. I have had the PSP since launch BTW.