You now control Cecil in battle in the opening sequence 
New flashback scene of Cecil/Kain dueling in Baron Castle 
Additional dialogue between Cecil/Rosa in Baron Castle bedroom (?)
 
Extended scene in village of Mist between Cecil/Kain/Rydia 
Rydia has a new companion, the Pochika 
Subtle map changes to towns and dungeons (ie: On the peak of Mt.Ordeals, instead of a small shrine, there is now a stone tablet which teleports you to a shrine) 
Namingway has a new job as Mappingway (changing names appears to be unavailable due to voice acting) 
Decant Ability System 
Auto Battle System 
Auto-map, rewards for 100% exploration per level 
Cecil cannot equip bows or staves 
Cecil gains more white magic spells (protect, shell, raise) 
New magic spells Ultima, Faith, Brave, Bubble 
Arrows are not consumed when shooting a bow, and come in quantity of 1 from chests 
Characters rejoin at set levels 
Tellah is now able to earn sufficient MP above 90, with sufficient level ups. (thus allowing meteor to be cast early.) 
Bosses are generally harder and have new attack patterns 
New Hidden bosses 
Kain and Palom are now right handed 
Item capacity increase 
Switching weapons mid-battle takes up a turn 
Gilbert can select songs to perform 
Bows are fixed on the right hand, while arrows are fixed on the left 
Bows no longer cause extra damage to flying targets 
Spears no longer cause extra damage to flying targets 
Child Rydia learns different spells over the long run 
Various characters have different stat gains 
Stat changes past level 71 are no longer random but controled by equipped decants 
Spell damage has increased for most spells 
Bio damage reduced 
Can use spells from the magic menu without going back to the main menu after each turn 
Every character except Cid naturally gains MP 
Edge can no longer equip claws 
Exit/Warp is disabled in all Castles and towns. (prevents bugs, like fetching the dark crystal early.) 
Warp is completely disabled in the Sealed cave. you now have to walk all the way back out. 
Warp now puts you at the start point of the previous room. 
Elixirs can now be bought (from hummingways). 
Bahamut's megaflare attack cannot be reflected.