Okay, so it's been on my mind ever since I picked Final Fantasy IV for DS back up again, and have gotten into discussions with friends/co-workers about various Final Fantasy games. Now, don't take this the wrong way, people - Final Fantasy VII was a wonderful game. I simply prefer Final Fantasy VI, and think that Final Fantasy VII got too much publicity because it was the first in 3-D.

I want to point out connections, but first this key reminder: Final Fantasy VI came before Final Fantasy VII.

Big Bad Evil Guy
Let us compare Kefka Palazzo and Sephiroth. Both are powerful beings capable of world destruction, formed by the infusion of each respective world's form of magic into them and driven insane by that infusion. They differ in that one is a mage (Kefka) and the other a warrior (Sephiroth), but both develop cults in their own name who believe that the end of the world by their god will be a glorious thing. They both act as the final boss of their respective games, and can be devastating when unprepared.
But - let's face it, guys and gals - Kefka WON. He actually achieved his goal of world domination by awakening the Warring Triad and stealing the powers of the Goddesses of Magic. He was destroying the world, bit by bloody bit, and the heroes could only clean up the mess. Sephiroth lost the moment Aerith started praying for Holy; correct me if I'm wrong, but does she not come out of the Lifestream to finish the casting and eliminate the threat of Meteor at the end of the game?

The Lost Hero
Terra Branford, when compared to Cloud Strife, may seem boring. Still, we compare them: Both are infused with magic (Terra being half-Esper, Cloud being infused with Mako), are skilled swords...people, and both have mental problems - Terra's amnesia, Cloud's breakdown - which must be cured by allies (Locke brings back Maduin, while Tifa Lockhart restores Cloud's mind). Cloud's got the gargantuan sword thing going for him, but really, should he be all that superior to a half-naked girl that goes Esper? And this is coming from a gay guy!

It's Not Over Until Nobuo Uematsu's Last Battle Song
Dancing Mad: Four different tiers of dramatic music, each piece fitting the combat segment where it plays. The last one even includes Kefka's trademark maniacal laugh - this guy is a god, and impressed as he might be, he's so not afraid of you. He laughs in your face.
One-Winged Angel: Wonderful piece, complete with Latin words that, when translated, fit Sephiroth and his mission to a T. Fanboys, even me, memorize this song (and sometimes get weird looks as they sing on the parking lot). Anybody who's played Final Fantasy VII will recognize this tune.
The Rant Here: Dancing Mad gets less than the love it deserves because the Super Nintendo/Super Famicom didn't allow for lyrics. PlayStation did, so One-Winged Angel gets the edge by default.

Cast and Issues
In Final Fantasy VI, the player is treated to a total of fourteen characters and backstories - and that's just on the heroes' side! Each one has a hometown, a life they lost, an issue to call their own, and nobody is shoehorned into a particular part. Some of the histories (Shadow!) are difficult to discern without actual, focused playing time, and piecing together the immense storyline is rewarding in itself (especially when finding everyone in the World of Ruin).
In Final Fantasy VII, you get a total of nine characters, and one dies after one disc. Their personalities are a bit stronger, but that can also be construed as a way to assure you of their differences because, thanks to the Materia system (a good system; I'm not opposed to it), allows anybody to do anything.
As for issues that can be translated to the real world... well, that's a toss-up. They do teen pregnancy in Final Fantasy VI (Duane and Katarin in the World of Ruin), death of the innocent in both (though Aerith in Final Fantasy VII is far more poignant), and the rape of the earth and its natural resources in Final Fantasy VII (seen throughout the start of the game; ShinRa's use of Mako). Your call here.

Humor
Final Fantasy VII is too dramatic! (Only Final Fantasy VIII is worse in this respect.) The comedy relief is a Turk running a toy (Cait Sith) by remote control, and sometimes a foul-mouthed character - Cid Highwind or Barret, take your pick. (Though, there is one rather interesting series of scenes which winds up with Cloud cross-dressing and he, Tifa, and Aerith all threatening to mutilate Don Corneo.) In Final Fantasy VI, they utilize bits of humor throughout the drama: Edgar Roni Figaro, the womanizing king, is often poked at; Mog the moogle takes a tight control of the yeti Umaro; quick-witted Relm Arrowny banters with her adoptive grandfather, Strago Magus (the old 'fuddy-duddy'... the entire scene where Sabin Rene Figaro walks half the world and winds up alongside stuffy, mechanophobe Cyan Garamonde and wild-child Gau - their conversations are at times hilarious! ("Thou art such a pain in the... Confound it all, I'm starting to talk like you!")

Setting
This is far more based in opinion, but I want to state it, anyway. In Final Fantasy VI, you have a mostly medieval-styled world. There are some modern accoutrements (Narshe, Vector), but never anything to make the world truly modern... and then, there's MagiTek, which the introduction and some other story elements revolve around. Technology is a Great Skill, reserved for machinists (Edgar) and serves to make the story and world more fantastic (submarine [subterranean?] castle, airships, aforementioned MagiTek). Magic is introduced slowly, and its role is slowly revealed, making it at least slightly mysterious.
In Final Fantasy VII, magic is a tool in the form of Materia, people fight over the Lifestream (which is the source of magic), and the world is essentially modern all over. Almost realistic, at times (ignore the guy with the cannon for an arm and the giant sword). The world could almost mirror our own, in some sense.
I prefer Final Fantasy VI's more medieval look (and its post-apocalyptic look). Final Fantasy VII... I don't know, there's a lack of something that makes me less into it. Things that should be special just aren't anymore. The characters can share abilities that were once limited to certain classes. The special-ness just kind of, I don't know, fades.

There's more - I'll edit as I think of it. For now, though, these are the reasons why I prefer Final Fantasy VI to Final Fantasy VII.