PSP hands down. Aged better for one thing. While both are great. PSP is underrated with the insane arcade and RPGs on the system. Also have my fave game of all time...ok so does DS but PSP has the best version. Ys 1. PSP 3000 screen still looks nice. DS screen...eh. DS is a fantastic machine. I enjoyed the hell out of it but while the PSP doesn't have as much. What I do have I enjoy more overall. It also has one of the greatest remakes/reboots of all time. Ys Oath of Felghana, which is a remake/reboot of Ys III. My god what an improvement. Plus that soundtrack holy shit!
PSP has one of my fave Saturn games on it. Princess Crown which is a pre-cursor to Vanillaware games like Odin Sphere and Dragon's Crown. This is essentially their first game. After Atlus made PC, the bulk of the PC team left Atlus to form Vanillaware.
I'm currently playing Crisis Core on PSP.