They're almost completely the same games. The FMV is just before you even start the game and one at the end, but they're not even proper in-game FMV.
If you want to play another version of the game, I would consider FFVI Advance on GBA to be the best version out so far. It has an overall better translation for a lot of things as well as a couple of new areas, four new summons, and three new spells. It also contains bug fixes, including fixing the Evade bug (Evade does absolutely nothing on the SNES version; MBlock instead determines both physical and magical evasion). The FMV are not on this version.
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