The PS version of FFIV is contained in FF Chronicles, which also contains the excellent Chrono Trigger. Both games feature new FMV sequences not found in their SNES versions. So if you want to play FFIV, make sure you get FF Chronicles.
The SNES version of FFIV was called FFII in the US (it was never released here in the UK). So if you can't get FF Chronicles, look for FFII for the SNES but this version is a watered-down version of the original FFIV.
If you want a more accurate English translation of the original Japanese SNES version of FFIV, you can download the translation patch from:
http://www.zophar.net/newtrans/?op=show&type=snes
That site pretty much has translation patches for almost every 8-bit and 16-bit game released.
But as Red-Mage has suggested, you might want to hold out for the GBA version of FFIV, which will have more improvements over the PS version... but I'm not sure if it'll have FMV sequences though.