For those who have played PSP version and the DS remake version....
Just for information, I know noone here brought it up, but just like talking about that stuff. It's a common misconception that people think that FF4US was the same as the JP Easy Version.
There was 3 versions of FF4 out there, in order they came out : FF4JP, FF4US, FF4JP EZ Type. There never 'was' a Hard Type, it was just the standard difficulty.
The FF4US version came out before the EZType version was in Japan, and while it most probably used the FF4US as a basis, it wasn't exactly the same. Some slight differences like Ribbon having the property to absorb all elemental damage (Rydia cures you with Thunder 3, booya), to a new sword that you could find before the Magnetic Cave, called the Piggy Sword. It's not considered metal, boasts pretty high attack power, and to make it more surreal, randomly transforms monsters into pigs (o_O).
The graphics of the last boss was also changed for some reason, and was reused in the GBA/PSP extra dungeon, which is where the "Zeromus EG" comes form, EG standing for Easy Game or something the like. Of course, it's ironic because that Zeromus is actually somewhat harder than the original.
That said, the only 'easy type' the USA ever received was the SNES version. All other versions (PS1, PSP, GBA, DS) were essentially based off the standard version. Yet there was oddities about the GBA version, such as the oddly missing difficulty for the first few hours of the game. The game seems to have been dumbed down, even compared to the SNES, until you reach get your airship. Alot of random encounters monsters simply 'forget' to attack. I don't remember being able to kill off 6 Goblins with Cecil solo without any of them attacking once. Yet it happens on the GBA. And it happened on the PSP version as well. After that, the difficulty becomes decidely more brutal, especially if you tray to ransack Old Elban castle before pumping up quite a few more levels. I'm pretty sure it wasn't that hard on the SNES, yet it's giving me troubles on the PSP.
The NDS version though is oddly different, in a good way. Even for those that know everything about the game, the NDS versions throws you quite a few curveballs, mostly in how the bosses behave. They changed some of their elemental weaknesses, some of their behavior are different, like the 'gas' Dr Lugae uses that turns damage into healing and healing into damage, or (which was a murder for me) Leviathan's opening with Tsunami before you can take a single action. Spent most of the fight trying to stay alive after that.
Most of the difficulty can be offset with smart use of the Augment system, but its not something easy to figure out on your own without guides. A few of them are obvious, like Cecil Draw Attacks. Others are just using your judgement depending on your playstyle. And getting all Augments is not very obvious either as you sometimes sacrifice decent augments to get better ones.
It was a breath of fresh air for a game that most already knew by heart. If they remake FF5 and FF6, I want them to do it like FF4NDS. Not graphically speaking, but adding new stuff and changing things to keep my on my heels.
There was a thread a while back where they dug into the rom and discovered that most enemies had their stats lowered in the GBA version for some inexplicable reason. The oddly low difficulty in the GBA and PSP versions was popularly thought to be an ATB related bug, but it isn't. Most of the monsters had their speeds, and in some cases other stats too, nerfed significantly. I have no idea why, it virtually ruins the pacing of the game and makes it much less satisfying.
This version is in fact much easier than even the easy type FFIV, which in turn was slightly easier than the American FF2. You can tell a pretty dramatic difference if you play them back to back.