All the tiny little differences could probably fill a book, but know that generally updated graphics and added features have been added (such as collections, like Bestaries, and bonus dungeons with new items and enemies). Here's some of the features off the top of my head:
Final Fantasy Origins (Final Fantasy I and II, PlayStation)
Difficulty options for FFI, and fixed bugs. Otherwise, both games are the same with the addition of some configuration settings and Amano artwork and item collections. Hosts updated graphics and near-orchestral quality rearranged soundtrack.
Final Fantasy I and II (Famicom):
Just the first two games combined in one cartridge.
Final Fantasy I, and Final Fantasy II (Wonderswan Color)
Same games with updated graphics.
Final Fantasy I and II: Dawn of Souls (Gameboy Advance)
Graphics comparable to that of FF Origins. Extremely downgraded difficulty. Bonus dungeons with extra equipment and an additional storyline for FFII have been added.
Final Fantasy III (Nintendo DS)
Completely rehauled graphics in 3D, and rearranged sountrack. Not a mere port with extra content, this is a bona fide remake. Rebalanced job system and extra features that implement the DS' WiFi features through a messanger called Mognet have been added. Enemies are tougher as fewer enemies appear in battle due to graphical limitations.
Final Fantasy Chronicles (Final Fantasy IV, PlayStation)
-Better translation, and restored items and difficulty. Story is actually coherent now. Major loading times during saving, but nothing to worry about elsewhere. Memo save feature added. Otherwise, exactly the same as the SNES version.
Final Fantasy IV (Wonderswan Color)
Exact same game, but with updated graphics. Only released in Japan.
Final Fantasy IV Advance (Gameboy Advance)
Wonderswan graphics. New and improved menu portraits. Party member selection is available after a certain part of the story. The new dungeons the Cave of Trials and the Lunar Ruins host new equipment, puzzles, and adversaries. However, there are a few bugs such as the faulty ATB and the ability to make the new superboss a complete weakling. The overall difficulty of the game seems easier due to speedier battles and the dash option.
Final Fantasy V (FF Anthology, PlayStation)
Horrible load times and an abysmal translation plague this port of Final Fantasy V. Otherwise the same game, but not really worth playing. You'd be better off with...
Final Fantasy V Advance (Gameboy Advance)
Retains the original's difficulty and has a sharp, new translation. Four new classes and a bonus dungeon are added. Menu Portraits have been added(during test, the characters' sprites still appear on the menu), although not everyone seems to be pleased with them. A true port to a great Final Fantasy.
Final Fantasy VI (FF Anthology, PlayStation)
Horrible loading times. Re-uses Woolsey's original SNES translation, yet gives him no credit...Also, the sound quality has been lowered, and the game is just plain slow. While there are nice features like the beautiful FMVs and the completion gallery, this isn't a must-buy game. Better stick with the original or...
Final Fantasy VI Advance (Gameboy Advance)
Lower resolution graphics, due to trying to fit things into the GBA's screen. Drastically lowered sound quality due to being ported to a handheld as well. New menu portraits for some NPCs during text. Many notorious bugs like Vanish/Doom fixed, while some lesser-noticed bugs remain (like Kutan). Four new Espers, Gilgamesh, Leviathan, Sabotender (Cactuar), and Diablos have been added. Bonus dungeon added. Not all new additions are known at the moment, but this is nonetheless a hotly anticipated remake.
Whew, hope that helps you.
