Honestly, I wish there was an "All of the Above answer" because there is very little I don't like about FFVI.
I end up saying character/story because I do love the cast and story, as well as the world and mythology that goes with it. It was the first game I ever played that didn't try to play up the "ye old medieval" style fantasy, and at the same time, it never made a fuss about the sci-fi elements either though that was pretty normal for FF at the time. I just like the concept of the old myths and powers of legend not being a real myth and in fact magic is real, but it's a power man can't really control. Yes, there is an evil empire but the heart of the story is about man's folly with dabbling with things it really shouldn't be trying to control, and the idea of the corruption of power and history repeating itself. The War of the Magi may have been 1000 years ago in the story, but it's effects and lessons are still so profound in the world that the character in the story sometimes make you think it was only a few decades ago. I like the idea of the espers and their own take on humanity and the war and I felt the Magitek Factory and Magicite concepts were both dark, creepy, and smurfing awesome. I still get moved by the characters and the memorable scenes in the game, from the opening of the game, to Cyan's watching his family board the Phantom Train, to the Opera scene, to the end of the world, to Shadow's dreams, to Celes' suicide attempt, to Setzer's flashback, to Locke's reunion with Rachel, to Terra fight for the kids of Mobliz and the awesome final battle and ending. It's all good.

At the same time, the game didn't get too caught up in it's dark elements and had plenty of humorous moments especially with silly side villains like Ultros and comical shenanigans like the entirety of Gau's recruitment.
The graphics do an amazing job of showing off something darker than previous installments, and they did some pretty cool things with the Mode 7 effects from the awesome airship flying, to the opening scene, where you see the Magitek Armors march onto Narshe in a snowstorm, and chocobo riding! The bigger and more detailed sprites allowed for much better design choices, with the game going for a Victorian era style with some of the clothing options, really noticeable in Jidoor. The architecture of the building was also neatly done though Vector and Narshe really stand out as the eye popping cities in the game. The better colors and details also allowed Nomura's monster designs to really stand out with magnificent creatures like the Hell's Rider and Amano's Number 024. The magic effects are also pretty badass, VI still has my favorite versions of Quake, Ultima, Flare Star and Alexander.
The game mechanics quite ahead of its time, and was really the first sign of the type of customization hi-jinx we get to see in the later entries, but I also like that the game combined FFIV's pre-set classes with the deeper customization options on par with FFV's job class system. It really was a marriage of the 16-bit era's innovations. The skills allow the characters to have more personality and purpose in battle, but the ability to teach magic, raise stats, and the importance of equipment and relics allow for some really deep customization. It's one of the few games in the series where I really felt they did a good job giving the player options and preferences for play-style. The game also has wonderful use puzzles and deliciously evil dungeon design like Gogo's Lair, Narshe Mines, and the team split up dungeons like the Phoenix Cave, Kefka's Tower and Dragon's Den really kept the game feeling fresh and entertaining throughout. Honestly, I feel FFVI has the best overall dungeon design in the series, yes I said it and the haters can suck on it.
The music is easily my number two option because it does so much to add personality to the game and really sets the mood; not to mention Nobuo got the SNES to really step up and perform some music that seemed impossible at the time. I have yet to be impressed with a soundtrack quite as much as this game. Seriously, it has some of the best character themes, wonderful scores that can make you
laugh,
cry,
feel heroic,
terrified, inspired, and
totally in awe. I still argue its the best OST in the series, if not in gaming overall. No other soundtrack has so many good compositions, and not other OST has ever done so much to add so much to the story and gaming experience overall. It's no surprise this game has more tracks than any other OST in the series that has been mixed and arranged and used for albums and concerts. It is just so memorable and it was pretty groundbreaking at the time cause despite being just midi quality, Uematsu was able to make the game "sing".
Mog is also awesome and he's still the best moogle in the series, hands down.
So yeah, I'm going to say it's really the whole package here, because each element works with each other to create something truly magical.

:ffvipatpat:
