They both have their merits. The DS version has had its randomness balanced, but I've also heard it described as being too balanced. A good example is the Farsight Bracer, which is an item that when worn will always let you see the entire map immediately, as well as the activity and placement of all the enemies. If you know how to fully make use of it, this is enough of an advantage to single-handedly win you the first quest all by itself. In the DS version, it only appears in the last half of any dungeon, whereas it can appear at any point in the SNES version. I had one play-through where the game spawned me two spaces away from the bracer in the very first room. The odds on that happening are astronomical, but those kind of truly random possibilities are what I personally prefer. One thing to keep in mind is that my item manager only works with the SNES version. However, there are plenty of checklists online for the DS version if you choose to go that route.
A pretty big difference in the DS version that can be seen as a positive is that the final 99 level dungeon reworks the last fifth its rooms. In the SNES version, level 79 contains as powerful an array of enemies as will exist until the end. The DS version creates a few more power evolutions that can make the last leg a bit more interesting. No matter which version you choose, I'll give you two good tips to get going. First, If you visit the Tavern in the town before each outing, the bartender will always give you a rice ball to stave off starvation. Second, you can visit Fei the researcher before each outing and test one of his tutorial rooms. Not only does each one teach a VERY valuable lesson about the game's possibilities, but afterward he'll also always give you an item to take with you on your main journey. I know that in the SNES version, the item he gives is drawn from the entire pool of items that are available in the first quest, so this can be a huge advantage.