The DS, there are some 40 games I own on DS yet not half a smany I would even consider buying on the PSP.

ds hands down

DS, I stopped playing my psp after I beat Star wars battlefront 2, I know there are a lot of good quality titles for the psp(God of War: Chains of Olympus,Crisis Core: Final Fantasy VII)but they either don't appeal to me or I don't like them the only game psp game I am interest on getting is Kingdom Hearts Birth by Sleep since I am a Kingdom hearts fan, I think I would have enjoyed my psp a lot more if my stupid bastard friend wouldn't have lost it and instead give me his fuck up psp which has the screen broken so right know I don't own a psp and I don't think Kingdom Hearts Birth by Sleep will make me get one.

On the other hand I love my DS Lite(I used to have the original style one too) the last game I remenber playing was Zelda back in November I have just notice that all my DS games are 1st party so from now on I will start supporting 3rd party games the one's that I want the most are The World Ends With You, Kingdom Hearts 358/2 Days,Final Fantasy IV,Ninja Gaiden Dragon Sword and Dragon Quest IX .

So in my opinion the DS has better games.

I think this is a pretty fair analogy:

DS = PS2
PSP = Gamecube
Switch Nintendo's and Sony's first party games around.

Both have lots of great games, but it's pretty clear which one has the most, and the only way to disagree is to vastly prefer the type of first party games on the other console.

For me the ds easily, a whole lot of niche games that really appeal to me are on the ds (etrian odyssey, izuna (though I hate to admit it), nanostray 1+2, hotel dusk, trace memory, touch detective, viewtiful joe)
plus plenty of more mainstream games, RE:ds , Call of duty 4, brothers in arms (these 2 seem really under appreciated) advance wars, age of empires,
great legacy games like Castlevania, Metroid, Sonics, and Marios
licensed games that inexplicably aren't trash like transformers, tony hawk's and the spiderman games
plus it has Contra 4, so even if it had no other games I cared about it'd win
plus this isn't a comprehensive list of ds games I've enjoyed,
not to say the psp is a slouch in terms of good games, but it doesn't have the diversity and volume of the ds basically I've only enjoyed a few original games Jeanne D'arc, Silent Hill origins, Sengoku cannon 3, Me and my Katamari, and that's it, but collections and remakes have been fantastic for the system

According to metacritic the psp has better games than the DS, by almost a long shot.

It has more 80+ ranked games than the DS by I think 10 or so. Though the thing is the DS has more games, just not as good as the psp.

In my opinion the psp has better games, simply because of god of war and FF VII, and other GTA/ platforming RPG titles, I play my psp much more than I play my DS, haven touched my DS since I took the picture to show that I had a DS, and that was around august last year.

The Thing is i think both have great games, but when it comes to being a handheld the DS takes the crown, i was playing ninja gaiden on the ds the other day, and for real i think that one game is better than anything that can come out for the PSP, if more games like ninja gaiden and Zelda (great touch screen controlled games) come out, the PSP will have nothing on the DS, and to be fair judging by sales there really i no contest. The thing is my brother owns a psp, and its been laying here on my bedroom floor, 4 like 6 months.

Both do have good games, but I say DS has more good games, First Party games and more support from Third Parties.

PSP by a mile.

DS doesn't have good games that I like. Its only games I like are New Super Mario bros, Mario Kart DS, and pokemon diamond/pearl. The other games just aren't good. Of course this is my opinion and not DS bashing.

PSP has God of War, 2 Grand theft auto games, Star wars battlefront, socom, lots of good racing games like need for speed underground rivals, daxter, hot shots golf, metal gear solid, and more.

PSP.

not because i liek sony, because i can play some ps2 prequels or sequels on it, an i can play fifa with better graphics.