Although I'm not a HUGE fan of the 3D-ness, it still came out to be one great remake.
I found that it takes a lot of stress away, not having to worry about class and/or character choice, giving you the characters according to the storyline. Another thing very stress-relieving is that you don't have to deal with long training sessions to continue on through the game. As long as you don't escape from the majority of random encounters, the next part of the game will be achievable, but not too easy.
Also, there were a few additions added on in the DS game. There was the introduction of augments, which give your character abilities otherwise unavailable to you, and a few good bonus bosses to try out. (Unfortunately, you would have to wait until your New Game+ game to take them on.) Also, there's the new Summon of Rydia's named Whyt, which is an interesting - if not very useful - customizable Summon that you can boost by playing several minigames.
The cutscenes were also very well done. Again, once you get past the flat faces and short bodies, they are more than enjoyable. Square also did a very good job with the voice acting. Some of the voices were a little unexpected compared to what one may have imagined in any of the earlier games, but they all fit perfectly.
All in all, it was a very good game. I enjoyed it SO much more than the last Final Fantasy remake (which I will not go into) and will continue to thoroughly enjoy it's replay value.