With regards to the pixel remakes, I hesitate to say they're running on the same hardware as the originals, for the simple reason that they're not subject to the originals' color palette limitations - the NES was simply not capable AFIK of handling backgrounds or enemy sprites with as much color variation as the ones on display here. Its not a coincidence that backgrounds were solid black with a little wallpaper at the top on the NES final fantasy games.
Look at the first post, where you can see the PR red mage sprite and the NES red mage sprite beneath it. The PR sprite has black, red, dark red, white, grey, two shades of yellow, light blue, and two shades of caucasian skin, ten colors. NES RM courtesy of 8 bit theater has exactly four colors - red, white, black, and Caucasian.
Except that's not quite right. See, sprites on the NES were limited to four colors, it was not physically possible to have a block of 8x8 or 8x16 pixels (the only two sizes available for sprites - anything bigger is multiple sprites in a trenchcoat) to have more colors than that available. And transparency counts as a color - the "black" in the classic FF sprites was almost certainly transparent, else they were using up limited data space (they could only have so many sprites on screen at once!) for outlines. This is where the black backgrounds in FF games come in - by setting the background to black with some color set dressing on top, "transparent" can be made to read as "black", giving you a fourth color for your sprites at the cost of one less color for your backgrounds.
This is why, incidentally, NES sprites tend to look so garish - they literally did not have data space for something as complicated as "multiple shades" unless they could have those shades be the ONLY colors. Its also why only some NES games had outlines on their sprites - they wanted to use that color for their scenery.
