Final Fantasy VI as compared to the others
FF6 did have some great twists, namely when the world effectively ended and your party was broken up and like you mentioned, finding out that Shadow is Relm's father. Shadow was also an AWESOME character. He may have seemed cliched but I think there's more to him than that. He worked for money and it seemed like that was his only motivation but in reality he was with the party more than anyone--he was willing to sacrifice his life to save them. Another scene that really REALLY moved me the first time I played (granted I was very young but I still like thinking about the first time I saw it) was the opera scene. Granted it was a story within a story, but ironically, I think the thing that moved me the most was listening to that music and watching Celes throw the bouquet of flowers off over the balcony, pining for her lover and watching the shooting star in the background. That did it for me, but maybe I'm just a romantic (no, I'm not). Kefka was also a great character but more than him, I liked Emperor Gestahl. I had such ambiguous feelings for him. Also, the love story was SO subtle between Locke and Celes that it was just awesome--not overt like in the later ones, although in my opinion it can be done well (X) and poorly (VIII). The gameplay was of course great and sufficiently challenging, although it is hard to say challenging when it comes to an FF because of course my characters' skills matter more than mine.
But as compared with the other final fantasies (I know this conversation has probably happened a bunch), I thought it was roughly the third best. (I've played 1-10, X-2, Mystic Quest, and Tactics and have beaten all of them except 3 (Japanese version) because the guy who put together the ROM stopped translating the text about 8 hours into the game.) Final Fantasy VII I thought had the best storyline for sheer intricacies and the fact that a lot of it was left in to be found in the subplots. There wasn't much to be found in the subplots in VI--for example, finding Sabin's master or Umaru or Ultima but once again, Shadow-Relm was a subplot sort of and was nice. Further, Final Fantasy X I also thought had a solid storyline and despite what many say, I thought Tidus was a great character for his ambiguous feelings towards his father. But those alone didn't pull FF X above FF VI. In my opinion, FF X had one of the best endings in a video game ever.
*spoiler start*
The two main characters' dying at the end is the plot twist of the century. Auron was the badass about it. Tidus, sad about leaving Yuna but accepting his fate, wraps his substanceless arms around her and then jumps off to meet his father.
*spoiler end*
The only problem was there was one FMV where FF X's love story beat you on the head with a club. some subtlety, please. As far as the other ***. I thought the love story killed 8 and due to Card Mod, Card-to-Item, Item-to-Magic, and the junction system, it was by far the easiest final fantasy ever. I thought 9 was good but for some reason I can't see the replay value that the others have. (If anyone can clue me in on why this might be, please send me one.) FF I was terrible (no plot, weak gameplay), IMHO, but back then I can imagine it was good. I'm going to lump FF II, FF IV, and FF V into good gameplay, okay plot but not as good as FF VI. FF III (Jap), like I said, I haven't finished so I cannot make an accurate judgement as of yet. FF Mystic Quest, I enjoyed when I was young but looking back it was poor. Finally, FF Tactics was damn good, providing a great challenge and a good plot with strong comments on religion (specifically Christianity) that I am surprised did not cause riotous controversy.
Those are my preferences and my reasons. Think what you will.
Locke was my favorite character! I also loved the graphics in FFVI. Seriously, when I first played FFVII I thought the graphics were actually WORSE. I was like "What the hell, why do they have squares for hands?".