VI - Desperation Attacks: This one people forget about, but it's technically the first "super move" system in FF. It's probably the worst though, because it's so rare and unimpactful. It has a low chance of randomly happening when a character attacks at low health, and VI is pretty easy so you're probably not going to have characters in low health for very long or often. They can do a good amount of damage given their high base power and fact they ignore Defense, but given their randomness and how easy it is to do stupid amounts of damage in the latter half of VI with more conventional methods, it's not worth trying to fish for these as a strategy.
VII - Limit Breaks: The classic. It's easy to say it's the best version of super moves, especially since VII is my overall favorite FF. They're flashy, useful, and the Limit gauge mechanic is simple enough. There's a kind of balance to it in how the gauge fills up based on taking damage, so it's kind of a comeback mechanic in a way. If you're getting your ass kicked then you'll see more Limits, but if you can handle the battle fine enough without needing them then you won't get them as often. That said, the damage the latter half of them can put out it kind of unbalanced. Sometimes I've had Cloud's level 3 Limit available before the end of disc 1 and it can do like 8000+ damage at that point when bosses have no more than 10,000 HP. It makes it so if you're struggling with a boss you can just go in with a full limit gauge or two and blitz it to death without really engaging it, which is silly. Combined with how freeform the Materia system is and how easy it is to hit the damage cap, and it also causes the issue where technically Cloud/Barret/Cid is objectively the most optimal team to take against superbosses because their Limits hit for the most number of hits. I do like that they played around with some characters having mechanically different Limits like Tifa and Vincent, but Cait Sith is weirdly screwed over by only have two moves instead of the usual seven. And Red XIII is more low-key kind of screwed over since his best multi-hit Limit only hits 5 times, while other characters get like 15 hits. At least Tifa's Limit is really good in low level runs.
VIII - Special Attacks: Also called Limits Breaks in English, but that was the localization team trying to piggyback off VII some more. These didn't really have any special name in the Japanese version, and mechanically they're closer to the Desperate Attacks from VI. But it's possible to easily go into them by casting Aura on someone, so it's possible to spam these as a strategy. While they can look cool, mechanically I think these were poorly thought out. It's meant to be a comeback mechanic, but Aura makes that mostly irrelevant. And there's a massive disparity in how good they are between characters, which against gets you this situation where Squall and Zell are plain better than everyone else at endgame. Like you've got Squall's Renzokuken and Zell's Duel which are just multi-hit attacks that can do stupid amounts of damage, especially Zell. Then Irvine's Shot can also stupid damage, but you have to farm ammo to use it. Y'know, whereas Squall and Zell can just do it for free. Rinoa's Combine and Volley can potentially deal high damage, but are kind of awkward to work with. Quistis's Blue Magic is well, Blue Magic, there's useful utility stuff in there but it doesn't feel like they should be restrained to being super moves. And Selphie's Slots is just random spells. Technically The End can instally kill anything in the game, even Omega Weapon, but it's so rare for it to show up that practically Selphie's special ability is the worst of the bunch. Bunch like the rest of VIII, there's some ideas in there but it's very poorly executed.
IX - Trance: This a tricky one to think about. It's more like super forms than super moves, which a cool concept itself but not quite as immediately flashy, and more importantly, this system tends to get a lot of critics because it has this awkward aspect to it in that you can't control it. The Trance guage essentially works like the Limit guage in VII, going up as you're attacked, but it does so at a much slower rate (the rate actually depends on your Spirit stat, so those with low Spirit have it fill slower) and critically once it's filled it activated automatically, so you can't save it for later if it fills during an easy fight where it's wasted. So it creates this frustration in that it can feel like you keep getting it where it's not needed and never have it during boss fights. However, I feel like if we could do something about that issue then this system is overall the best balanced of all these super move type systems. What exactly the Trance gets you varies by character, and some are generally better than others, but they each fit with what that character would want to do anyway, and since each character has a set role, the differences in Trance don't determine how good a character is at endgame like you see in VII, VIII, or X. And some of the Trance abilities have some interesting application, especially Freya's. I think this system has the potential to be close to perfected, since it can be very useful while avoiding being overcentrizing like Limits in VII, the special attacks in VIII, or Overdrives in X.
X - Overdrive: Basically like Limit Breaks, except you can unlock alternative ways to fill up the Overdrive gauge besides taking damage. Some of which can make it potentially very easy to fill the guage up and spam Overdrives, though probably not something the average player will do during the main story. Thinking about it, Overdrives are fairly well balanced for the main storyline, since I don't think they ever get too rediculously powerful too early, like Limits could, and the guage fills up at a decent pace. You can do some wacky stuff with Rikku's Mix, but that requires a knowledge check like doing broken things with Blue Magic or Mix in V, so I think it's fine and cool. The issue I guess is the systems around it in X, where maxing everyone in post-game puts you in that situation where Overdrives are the main difference between characters, so Tidus, Wakka, and Auron end up the best because they have the most damaging Overdrives, next to Rikku with her utility from Mix. Meanwhile, Lulu is screwed by having a magic-focued Overdrive with the most annoying QTE, and Kimahri has really underwhelming Blue Magic. Again, Blue Magic really shouldn't be locked behind a meter.
XII - Quickenings / Mist Knacks: I actually don't have much to say about these, because despite 100% completing XII, I barely used these at all. I haven't played any of the updated versions of XII which tie these to their own guage, but in the vanilla version of XII you had to blow all your MP to use these, and the damage on them isn't so amazing that that it ever felt like a good trade-off. Especially since the QTE to chain them together can be really annoying. I don't know, they just kind of feel a superfluous system to me, like XII would be just fine and barely changed if you completely removed them.