I think DS easily wins:

IMO PSP has several good JRPGs, while the DS has dozens upon dozens of them.  

I'm not sure I actually prefer one over the other. On one hand, I absolutely love the SRPG offering on PSP while on the other I love many remakes/ports on the DS.

Both have some great original games - namely TWEWY, Jeanne D'Arc, Crimson Gem, Dragon Quest IX, etc...

PSP has an extra Disgaea port - which carries heavy weight with me. DS has FF IV - my favourite game.

On the horizon, both have a game that I'm really, really hyped to play - Valkyria Chronicles 2 and Ninokuni.

Not trying to sound overly diplomatic or anything, but I think I like them pretty much the same in regards to JRPGs.

I don't think I can vote.  Both of them have such a steady flow of rpg's that I can't really decide.  I'll go ahead and say that the PSP's jrpg's are more visually stunning and more likely to feature voice acting but if you're playing an rpg for the graphics, you're doing it wrong.

I say flip a coin and have a blast.

DS in a HEARTBEAT.

It has:

- The World Ends With You = An extremely innovative take on the JRPG genre in terms of its battle system. It has a very gripping story and nice pace in terms of plot. The music was great too.

- Shin Megami Tensei: Devil Survivor = An excellent JRPG which mixes an RTS type battle system with a  traditional turn based one, seeing both forms combine was a treat. But again its strong and engrossing story made me love it even more.

- Dragon Quest Remakes (DQV, DQIV) = I hadn't played either of these games and as soon as I played DQV it became one of my favourite JRPG's of all time. DQV was an amazing experience and made me a fan of the series.

- Final Fantasy IV Remake = Again an RPG I hadn't played till I got the DS. And it went straight into my Top 5 FF games of all time. Just loved the game, especially the music, charm and the style. The story was decent too.

Others that I liked on DS - DQIX, FF Tactics A2, Shadows of Destruction

So basically khuutra's description fits this battle.

PSP..PS1 JRPG Classics..nuff said.

But In all seriousness I like PSP's Selection Better.

Hey, watch it now! 

Locking by request.

This is definitely the highlight of this entire gen: handhelds.  

Both the DS and the PSP have kept us JRPG lovers happy this gen (especially with the lack of jrpgs on the HD consoles).

They both have heavy hitting JRPGs

PSP - Monster Hunter, Persona (remake and upgraded)  Disgaea (remake and new), Tales of

DS - Dragon Quest (remake and new), Final Fantasy (remake and new), Tales of

They both have great Atlus support (very important to me)

They both have amazing new IPs: DS Sands of Destruction, TWEWY, etc:

PSP:  Crimson Gem Saga, Jeanne D'Arc etc.

Ultimately I will vote PSP.  I have had it much  longer than my DS and until very recently I did not even want a DS (regardless of its wonderful library) because I never felt I needed it.  My PSP was giving me everything I wanted in a portable gaming system (besides a better battery life) with its great list of new IPs, remakes, PS1 classics and even PS2-PSP ports.  The upcoming line-up of both consoles is also amazing, but I still have to give the edge to the PSP.  Valkyria Chronicles 2 takes the cake for my most anticipated Handheld game.