I hate these kinds of wars, but I'd like to talk about the psp from a different perspective. First, let me say, I think the DS lite is very cool, but I only have space for 1 portable system. The following takes some money (having fun means buying memorysticks rather than games) but to me it's been really worth it.
OK, as for PSP. Having a PSP with the 1.5 firmware version is necessary. If yours is later than that, you can change it back to 1.5 using a free downgrader (which requires having GTA in your possession, at least for the 5 minutes it takes to downgrade). If you're into piracy, this is what you do.. then you can play any .iso file of a psp game, you can even stream games from your PC via usb or wifi if your memorystick isnt that big.
Once you go to 1.5, the entire homebrew library opens up to you, and free software called Devhook lets you use all of the later firmware when needed (for later games, for the web browser, rss, etc).
There are tons of homebrew applications and games (video players, graphical shells, ebook readers, etc).
And then the big thing for me is emulators. You can play about 85% of all NEOGEO arcade games fully, 100% of all NEOGEO CD games, sega genesis games, NES games, Turbografx 16 (and PC-Engine CD games up until the supergrafx system), basically every other old system there is. Atari ST computer games even run playable. SNES games generally run at close to full speed. There's a decent working MAME for older arcade games. The list is huge. Progress is steadily being made with GBA and N64 emulation as well. If you want to play older games (well a lot of neogeo games compete with today's games at least in 2D), this is great.
Next emulator: This year sony is releasing a playstation emulator that will support over 7000 original psx games.
Extras: internet support with web browser, rss, flash, etc. MP3 player, movie player (put video clips, movies, etc on your memstick to watch), etc. coming soon: GPS system, camera, keyboard, use as a special controller for ps3, ability to see the PSP on your TV.
Games aren't region-coded so you can import (or pirate) any country's games - if you like unique stuff, I think the japanese library is a lot more interesting than the US one which most people seem to complain about.
etc.