One thing's for sure: Both games have
killer basslines to their
boss music.
Super is closest to the original Fantasy Zone in terms of formula - no special environmental gimmicks, just buying stuff from the shop balloon, blowing up enemy emplacements, and fighting the boss. Nice and simple, and a solid entry - probably king before DX came along.
Original Fantasy Zone II is the one I've spent most time with and so have the most nostalgia for,
cacophonous main theme and all

The main change in the sequel is the addition of teleporters between different fields within each stage. This makes for a somewhat more obtuse game, since the player has no way of knowing how many zones are left, or where each teleport leads. Further to that, the shop is now fixed in place, and the boss is accessed via a special teleporter that only works if the whole zone has been cleared. The maze-y twist doesn't hold up as well as the other entries, but the stages and bosses are still good.
Despite being billed as a remake, the System 16C version is really more of a reimagining of FZ2 than a faithful redux; it sticks closer to the FZ1 structure, bringing back the shop balloon and relegating the teleport mechanic to a simpler light side / dark side switch. It's also more forgiving, since holding a weapon powerup lets you take an extra hit.
It's probably the most polished game in the series, but that's not a big surprise seeing as it was made by M2 with years of hindsight. Personally I didn't like the way they added slight intertia to some of the movement, but it's not game-breaking, and there's so much good stuff in there that it's an easy flaw to forgive.
It's also worth mentioning the
2.5D remake of the original Fantasy Zone from the SEGA Ages collection on PS2. It's mostly faithful to the original, with a few extras here and there like rail shooter post-boss bonuses and new powerups like the evil-looking bat wings.