Origins has art galleries that you unlock throughout the games and the best-quality graphics and music. Plus a couple FMVs and a treasure gallery that marks your progress in getting all the game's treasure chests, but they're not a big deal.

Dawn of Souls has four extensive semi-random dungeons with a ton of new enemies, items, and equipment to find, and that's just for FFI. FFII has a brief quest that's accessible after the beating the game once that brings some additional closure to the plot. Oh, and the dialogue is now accompanied by character portraits.

Both versions have detailed bestiaries for all the monsters you've fought.