Origins isn't identical to the original FF on NES/Famicom because Origin fixes all of the game's bugs like how half of the Black Mage's spells didn't work, or how the game never incorporated the Intelligence stat meaning the Red Mage could do the same amount of damage/heal as the actual dedicated mages, and the critical hit weapon bug was fixed as well. Origins is basically how the game was meant to be. This largely results in the class finally being properly balanced whereas in the original, the Fighter, Ninja, and Red Mage gained huge advantages while the Black Mage became utterly worthless.

Chronicles is the closest thing you'll get beyond emulating to the original FFIV gameplay. Sadly the translation, though better than the SNES version, is still cruddy. IV is actually pretty brutal throughout the game unless you grind (or accidentally grind trying to get the game's various rare item drops) to high levels early. It is also the only version that keeps the "steal the Dark Matter from Zeromus to change Big Bang from near-total-party-kill to something manageable" strategy. I'm still irked that SE chose to release the PSP remake on PSN and skipped the Chronicles version.