The rules are pretty vague on PSP emulators, but until you receive a response I would recommend playing Spyro 3 on a ps1 emulator, because the rules currently state that epsxe is the only emulator allowed, but you may get a response from a moderator verifying if that can change to accommodate PSP emulators.

Personally I know next to nothing about PPSSPP, but considering it's not designed for PS1 emulation I'd be very surprised if it stacks up to ePSXe or Mednafen in terms of accuracy. No reason to use it when there are good PS1 emulators out there.