It's much harder to compare the two games than you'd think. I've generally been under the impression that people quite substantially preferred VI to V, but I've never been quite able to make my mind up, though I tended to lean towards V.

In terms of story and character development, I'm going to go with the consensus and say that VI is a pretty obvious winner. That's not to say that V's plot was particularly bad just it doesn't stand out as much and isn't as good as that of VI. The characters in VI don't all get a bucketload of development, but those that do (Locke, Celes, etc) really make the game more interesting. The music in both are rather excellent. I don't think I could pick between the two in terms of music, actually. They've both some really excellent pieces such as Clash on the Big Bridge from V and Dancing Mad from VI.

Hard to pick, but I'd say V just edges it for me because, as has been said, it's more fun to play. Love the class system.