No current handhelds can run all N64 or PSP games. But the 351 can run much better then the 350. But for these the best is currently the Retroid Pocket 2, but although I really like the system it's design and build quailty and button/thumbstick layout isn't as good as Anbernic's. That's why I own both. Play the lower systems on the 351, and the newer systems on the RP2. The perfect solution would be to combine the RP2 inside an Anbernic case design.

If you want the best handheld for PSP, then a hacked Vita is the best solution by a huge amount. It's the only handheld other than the actual PSP that can run God of War perfectly f.ex. in fact a hacked Vita is the best solution as a handheld Sony systems setup as it runs PS1, PSP and Vita perfectly.