Pretty isn't it? XD
I own both, and both do have their ups and downs. (chances are you already made up your mind long ago XD)
~ PSP ~
Pros:
Screen - It has a nice large wide screen. Nice for gaming, you'll be able to see more on it.
Memory - Memory Sticks does sound like a bad thing for the PSP, you have to go buy cards when it runs out. But the thing is, it's not half bad. Around here a 1 Gig card is only $30 (that's at EBGames/GameStop). And with that you can save movies or songs to it.
MP3 Player - This is likely the most use I get out of my PSP. Get a large enough card and you got yourself a portable MP3 Player.
Web Browser - It has a built in Web Browser where you're able to surf the web.
Picture Viewer - You want to show off some pics from your last trip, or show off your new pet, just upload the pics to the PSP and you're set.
UMDs - UMDs hold more data then a DS Card. So they're able to put more stuff on a PSP game then what they have on a DS.
Graphics - There isn't much to say about the graphics, other then it being better then what you can find on the DS (the graphics of the PSP is somewhat in the middle of the PS1 and the PS2. It's not PS2 graphics, but it's close enough. If you want an example, look at pics from Tekken 5 for the PS2, and Tekken: Dark Resurrection for the PSP).
Cons:
Web Browser - I don't know if it's just my memory stick, or my internet or what. But for me, the web browser on the PSP is total crap. The loading times sucks, it doesn't support everything, it's hard to type (putting in a simple URL takes forever) and the screen isn't large enough to see anything. It's not worth wasting your time with.
Battery Life - I'll just put it this way, if you plan on getting a PSP I do hope you stay home with it or like bringing the AC Adapter with you and looking for an outlet, because the battery life of the PSP sucks.
Games - IMO the PSP just doesn't have the good games I would like. There are maybe 3 games I want ATM (and I only own one game). I just can't find any good games for the PSP.
Computer - Just about anything you can do on the PSP you can do on a normal computer or a laptop (MP3 Player, Picture Viewer, Web Browser, Video Player. On top of that, a computer has a way larger screen for all of that).
~ DS ~
Pros:
Dual Screen - The two screens on the DS works well on many games. You got games like Mario Kart where the bottom screen is a nice large map. Or in Diamond you use it for attacks and your PokeTech. Or in Metroid Pinball both screens act as one. And so on. Both work really well and adds something new to games.
Touch Screen - Try making a new emblem on MKDS using the D-Pad and A button. It'd take ages. Or get to the bottom of a long list of items for Pearl. The touch screen works really really well on the DS.
Games - There are a good many DS I want and I also got a good many. To me the DS is the better of the two when it comes to games. It pretty much has something everyone can play.
GBA Games - If you got GBA games and don't feel like pulling out your GBA/SP/Micro everytime you want to play them just play them on the DS.
Number of Systems - Lets say you want to play MKDS online. You got a better chance to find someone to race on the DS then what you would with a racing game for the PSP. The DS has outsold the PSP 2 to 1 so there are more DS owners out there and you'll likely have a better chance to play someone online.
The Price - The PSP Core is like $170 (I guess that's the price now). For that price you can buy a DSLite and a game. The DSLite is $130 so when it comes to the price you're getting a better deal.
Cons:
Graphics - The DS graphics aren't up to par with the PSP's. Sure the DS can pull off some lovely and great looking FMVs (look at Final Fantasy III), but it isn't the PSP when it comes to graphics.
Older Games - If you're looking for more mature games you'll find more on the PSP. The DS is more of a mini-game/quick play system.
Online - IMO the online play of the DS isn't as good as I'd like it to be. Little things like me wanting 2 on 2 battles (with 4 trainers) on D/P, more then 4 racers on MKDS. And I wish the searching and FC stuff was made better.
DS Cards - They can't hold as much as the UMDs can. So if you had a UMD sized game you'll be having a good many DS Cards.
Over all, I play my DS far far more then my PSP. I only pull it out maybe 4 times a year and then it's only to have a song play or something. If I had to pick one to go with it'd be the DS.