They run all the run same operating system, and honestly have pretty similar power...
at a push you might get N64 and Dreamcast out of the RasPi 3 but the real hardware would be so much better in those cases, none of them can run Higan so you have to deal with the meh SNES9X sadly, PS1 probably works a ton better on RasPi 3 and Mednafen PSX is a really good emulator. I know for a fact that anything 16-bit or less works perfectly fine on the Zero, and GBA support is good on the Zero too.
The question is size or performance? For a handheld you probably want the Zero W, unless you're building it in a Game Gear or something.