The PSP version is very close to the Dawn of Souls Version. They have some extra dungeons that allow you to fight later bosses in the series but little else.

The NES version is fun but I feel you get a little more out of the PS1 version cause it retains the originals difficulty but gives you modern conveniences like knowing how your equipment actually affects your party members as well as items that cast spells. Not to mention the spell list doesn't have the god awful translation so you actually know what all the spells are for purchase. The game also has a small gallery that unlocks original artwork and stuff the more you explore the game. As a bonus, like the DoS edition you also get a graphically overhauled FFII to boot.