The following is very long winded. I understand if you skip it. Everything below is my opinion. I do not present them as anything but my opinions. Take it or leave it.
There both kinda crappy, and yes i own both.
The games i have on my PsP that i enjoy are either remakes: Valkyrie Profile, Megaman, Old school arcade packs, Persona.
Or sequels of continuing series: Killzone, Crisis core, Dissidia, and soon KH.
My DS? The only games i ended up liking were Pokemon(Heart Gold, i hate the new iterations to the series) and kingdom hearts. There were other games i thought were okay but they were just spinoffs or remakes i later traded in for console games.
The DS DOES have an avalanche of games but most of them are hollow games and simple puzzle games. I don't feel like are worth the twenty bucks they charge for a flash game.
I'm not a huge fan of handhelds to begin with though but I am willing to admit i bought both simply for the Kingdom Hearts games coming out for them both(I'm weak and love that series).
Honestly having a small library like the PsP isn't any worse then having an avalanche of crappy games like the DS.
Does the PsP have a lot of Original games? No.
Does the DS have a lot of Original games? No. Yes yes i realize, SHOCK. Go check out your eb or future shop of wherever you buy your games. The majority of the games you find are just rehashes of other games. I counted sixteen different "pet" games my last trip to HMV. I count every "pet" game the same. Doesn't matter if its a pet hospital or pet training or Nintenpet its a game where you watch a freaking pet. Same with brainage and all its look alikes.
My EB has a wall JUST for Pet and brain games. With one shelf with a small rabble of other games. Most of which are point and clicks.
What am i going on about? Oh, right. Both sides are stupid. The PsP is flashy and sony clearly doesn't give a shit about the people who bought it way back when what with this PsP Go bullshit. Great Sony, fix all the bugs of the original but don't bother with giving us some way to recover all the games we already bought. KH will likely be the last game i buy for it.
The DS. Dear god the DS. So much hype. Well what do i have to gripe about it? Lets start with its flagship feature the touch screen. Nothing better then getting a cramp in my wrist because i wanted to play starfox. Most games i played that required the touch screen to play are the ones i returned either out of bordem or because i felt stabbing my touch screen for it to react half the time was unhealthy for it. The only games i ended up enjoying were the ones that ignored the touch screen feature or had it as an option. Pokemon had the right idea, use it as a convenience not a necessity. Now to cut off its other testicle lets go after the DS library. Yes i realize there are original games but a game is only original the first time. Like i already stated i don't count the millions of variations of PET or LEARN as new games when its fundamentally the same, damn, game. As well a lot of its actually neat and interesting games i ultimately felt were damaged by being forced(key word is FORCED) to use the god damn stylus.
Now, i realize i bag on the DS a lot. I realize it looks like i am more for the PsP. That couldn't be further from the truth. The thing is the PsP is like an empty box. What am i supposed to say about it? Should i make bring up its corrigatedness? How about i insult how brown it is, or the little up arrows on the side. Its a cardboard box. Big, sturdy, but hollow. Just like the PsP. I bag on the DS because i WANTED to like it SO FUCKING BAD. Ultimately i greatly despise its whoring of touch screen play. I feel not giving me the choice is bad.
The DS is that same box, but with wings glued haphazardly to the side. You just know there is a way to use that box well but people keep cocking it up and forcing you to use the wings when carrying it would be acceptable. Woooo yayyy its innovative! That's great now let me use the fucking D-Pad. Having to control Link with the Stylus the whole game irritated me to death. Mostly when i didn't draw half circles or whole circles well enough for his majesty link to do his fucking sword swipe and get cock slapped by a weak little mob.
In short both systems are riddled with flaws. The PsP could be great if Sony actually gave a shit about it and got some more unique and interesting games for it as well as advertise the thing in a non retarded way. The DS could be awesome if every time there was a good game for it they didn't force me to stab my DS like it was the man who raped and murdered my dog.
Wow.... Sorry... had a lot of hate in me... Good thing i got it out huh?