I would give you reasons why people think FFVII is better, but I don't believe it so I'd be lying. Hell, I'll just go with why I like FFVI more (in the same sort of format that omnislash and raskerino used).
1)Graphics: yes FF7 was impressive graphically at the time. I was as wowed as everyone else, but I find myself more impressed these days with what they managed in FFVI. All of the towns, dungeons and battle scenery looked amazing for a SNES game. Not to mention that they managed to show off more expression and emotion in those sprites than with 3D models that I can't help but love them. No game until FFX really managed to make the characters as visually expressive as that.
2)Characters: Yeah FFVII developed the backgrounds of all the characters pretty well, but looking back now, the only characters I found very interesting were Cloud, Tifa, Cid, and to a lesser extent Barrett. I just didn't latch on to many of the characters, and found that their back stories weren't all that interesting. Yeah it was nice to see that at least everyone had distinct and developed histories, but they didn't do anything for me. On the other hand, I loved the stories for every character in FFVI, and loved every character. I personally found that those characters had more interesting stories to tell than the characters in FFVII. Not only that, but it's about the only game where I can say I honestly love every character.
3)Story: I'm not going to beat around the bush here, I loved the story of FFVI more. You spend half the game trying to defeat the Empire only to fail, see the world destroyed and have to prepare for a showdown with perhaps the most psychotic villian in FF history. Not to mention that the story is packed with more than a few twists, and the great backstories for each character. I also like Kefka more as a villian than Sephiroth. I see him as almost the most tragic (and entertaining) character in the whole game. He volunteered to be infused with magic and went insane as a result. He didn't ask to become a mass murdering psychopath, he was made that way. And I also just have a soft spot for a villian who betrays those around him whenever it suits his quest for power, and revels in the slaughter of innocents. There haven't been many FF villians who actually did very much that was actually evil, but he kind of set the bar in that area. It wasn't a "this guy wants to destroy the world so you should hate him" thing, it was a "this guy did destroy the world so you should hate him" situation.
4)Battle System: Meh, both games were pretty easy, and generally involved every character learning every spell. I'll give it to FFVI in a heart beat though for giving each character unique skills thus adding a little variety. Yeah FFVII had limit breaks, but then FFVI had desperation attacks, and you can't use limit breaks all the time. Either way I prefer battle systems where each character isn't an exact copy of the other, and doesn't have the potential to come to that, but I still enjoyed both games battle systems and they certainly don't make me like the two any less.
Whether you like FFVI or VII more is all opinion. We could sit and debate the pros and cons for days but one persons pro could be anothers con. At the end of the day, I'm more than happy to just say both are great games and we all have our favorites, so does it really matter what anyone else says?