They only difference is that the PSX FF5 has 2 added FMVs; one at the beginning and one at end. Things that naturally went with the move to PSX from SNES were improved audio and control. Also, obviously, the text is translated into English. I played the PSX version, and enjoyed it very much.

Now, I'm not sure what you mean by "original" version - the SNES cartriage that came out in Japan, or the fan-translated ROM that you can download on a PC.

If you mean the Japaneses SNES cartriage, go for it if you can read Japanese, I guess, and have a working SNES that will play Japanese cartridges. If you mean the ROM, most diehard FF5 fans prefer that fan translation as opposed to the offical Squaresoft one on the PSX, but that's just personal preference.

As far as graphics (aside from the added FMVs) and gameplay go, the two are exactly the same.