Well personally I´d say PSP, I have one myself, it is useful for watching movies, manga (if you watch any), listen to music. It also has a couple of good games, and some quite good games coming up (Splinter Cell Essentials anyone?).
And then there is ofcourse...homebrew, both consoles have it. However the DS has very little, but the PSP on the other hand. It will add nearly everything you can imagine to your PSP, from fun little games, to a snes emulator, to a gba emulator, nes emulator, genesis, megadrive, SCUMM (Monkey Island, Sam&Max, Loom), name it and it exists. There are also PDA homebrew for the PSP so you can get stuff such as calculators, calanders, notepads etc. on your PSP. Lot's o' fun remakes of PS2 games made with homebrew (Dance Dance Revolution, Vector Infector etc.)
And not to forget the internet browser can be really handy at times too. I know, I know, the internet browser is also coming for the DS, but you have to pay 30 bucks for it or something like that.
So:
PSP:
Expensive.
Lots o' good homebrew.
Quite a few good games and alot more coming up.
Lots of things that the DS can't do.
Directed to people that want to do more than just gaming.
More mature games.
DS:
Touch screen
Cheap
Little homebrew capabilities(So if you played all your games, it can get boring)
Couple of things the PSP can't do.
Directed more towards just gaming.
More games for everyone, instead of just mature.
(You can talk about the DS all you want with it's upcoming features, but the PSP will still be better at them quality-wise. DS only as 120.000 colors, PSP has 16 million. Not to mention that Homebrew-wise, even though the DS is getting some better ones, PSP is still way better because of what the PSP is capable of (Processor-wise), It is really quite hard to emulate snes on the PSP, so it will probably be even harder on the DS. Well, it's not hard for the PSP nowadays, seeing as how you can overclock the processor to 333mhz, and the emulators work like a charm.)
So overall, get a DS if you are more into just gaming once in a while, not doing any other stuff.
Get a PSP if you are more of a multi-media kind of person, and homebrew.
Oh and by the way, Don't know if you like it, but there are rumors that the new PSP firmware 3.0 is coming soon and it will feature GPS and a camera on your PSP. (You do have to buy some stuff for it though, but the firmware update is always free.)
But if you buy a PSP, and upgrade it to 3.0 (when it comes out), you will not be able to use homebrew at the moment. Since the only supported homebrew firmwares are 1.00, 1.5, 1.51, 1.52, 2.00, 2.01, 2.5 and 2.6 (You are best to stick with 2.00 or 1.5 when you get a PSP, most homebrew work on those 2 firmwares, and the 2.00 firmware features the webbrowser, but 1.5 allows for more homebrew, and it is possible using homebrew to emulate 2.00 on a 1.5 PSP so you can use some of the 2.00 features on a 1.5 PSP (including the browser))