There is almost no difference between the FFIII(US) and the FFVI(JP) rom. Siren is nude, so is the picture boss. A few names were translated differently (Crusader=Jihad, Terra=Tina). Other than that, the games are nearly identical. FFIV on the other hand, is a different story.

I use SNES9x and it runs FFVI (JP) and FFIII(US) fine.