A hacked PS Vita (ideally a 1000 model for the OLED screen) is better than a PSP in most cases. With it, you can play both Vita and PSP games (and you can use plugins to play some PSP games with camera controls on the right joystick and/or with higher resolution), including homebrew emulators and games. People have also ported many old Android games to the Vita, some of which don't even run on modern phones. A PSP is only better in very specific cases:
- You want to use an UMD.
- You want to play an UMD Video (their ISOs don't work on Vita).
- You want to use a PSP hardware accesory (e.g. the GPS module).
- You really like the form factor of the PSP Go (other PSP models are really similar to the Vita).
With a hacked Vita you can use a cheap SD card adapter.