I think I already said this earlier in this thread but I prefer the DS version's music in just about every track. DQVI was already in my top 3 favourite soundtrack in the series but I really loved the arrangement in the DS version. It sounds more like the Symphonic Suite which is the energy and charm that I prefer in DQ music. The SFC version sounds more subdued. It's pretty much the same reason that I prefer the music in DQIV DS to DQIV PS1. I think I might represent the minority on that though.
DQVI DS is just a more refined version of DQVI to me. I know the scenario moves at a faster clip than the original but with the addition of party chat, they still feel fuller and meatier. The battle system is much, much better presented as well. Better sprites, better pacing, much better/faster animations. The interface is also much improved in general. The SFC game is really slow in comparison. Now it falls short as a remake because there's really nothing new to it, but it's a really good enhanced port!
Incidentally I finally got my brother to play DQVI (been trying for two years!) and I specifically asked him about the scenario pacing. He seems to like all of the scenarios and the rate at which they unfold so I think it's just a subjective thing. His favourite DQ games are still DQVIII and V, though.