Having played through both games, I can honestly say I prefer the original over the DS version. While the DS version fixed some issues I had with the original (Geomancer and Viking class are not useless yay!) I also realized it created other problems due to its technical limitations. Playing with Status magic for instance is key to surviving in the original because you are usually always outnumbered and things like the dividing enemies can and will murder you. Since the DS version can't fill your screen with more than four enemies at a time, it is far more manageable to beat regular enemies.

Also, I just prefer the retro graphics and music. I've listened to FFIII orchestrated arrangements for years before playing the original NES and I never was terribly impressed by the music but after actually listening to the original NES versions, I became much more impressed.