Thanks for this suggestion. I love SRPGs and somehow have not heard of this!
Most of the better games like P4G, P3P, Gravity Rush, Uncharted, Ys VIII, etc.. have been mentioned. I'll throw a few more.
- Don't forget Jeanne D'Arc, great SRPG game for PSP
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- Legend of Heroes Trails in the Sky FC/SC. Yes, PC version is better, but this is still quite good.
- Legend of Heroes Cold Steel 1&2
- Tokyo Xanadu (newer Falcom game). Yes, PS4 / PC version is better but this is still good.
- Odin Sphere (remake by Vanillaware)
- Muramasa Remaster (awesome action game by Vanillaware)
- Shinobido 2 - flawed but quite great
- Phantom Brave - quite fun PSP RPG
- Growlanser - great SRPG with quite complex story
- P3P (need to mention that again just because :P)
- Ys games (whole bunch, Origins, Celceta and 7 are really good, 8 mentioned above)
- MGS 2&3 HD and Peace Walker
There are a ton of great, great PSP and PSX games out there that are playable. And there are a lot of awesome vita games mentioned in the thread already and more that have not.