There is no perfect version of FFIV, unfortunately.
The SNES version is classic, but it is hampered by some severe gameplay changes that strip away a lot of the game's options, particularly in the early game.
The PS1 version is fully faithful to the Super Famicom original, with the original spritework and all of the original gameplay. Unfortunately, it is badly emulated with long loading times. I like the original difficulty though; regular enemies can pose a serious threat to your party, which keeps you on your toes.
The GBA version has some sound issues, but is otherwise similar to the PS1 version, I think. This is the one version I have not played.
The DS version really spices up the gameplay for the better. Bosses are much more complex and exciting, while the augments give the player a lot more options. However, the cutscene direction is absolutely terrible, and I don't think the 3D models look as good as the old sprites. The DS version also makes some changes: weapon selection is more limited than in the old versions (Cecil can't use a bow or staff anymore), and some dungeons (such as the Antlion's den) have been noticeably simplified.
I've only played a little of the PSP version, but it is immediately apparent that they seriously reduced the difficulty. The random monsters and first boss pose significantly less threat than they did in the already nerfed SNES version of the game. The new spritework is passable, but it doesn't look spectacular either.
What I would give to have a proper translated version of the original Super Famicom game that was actually well emulated. Maybe throw augments and the DS version boss changes in as well.