Final Fantasy I II Dawn of Souls was actually released before the Finest Fantasy for Advance was announced. Returning to the roots of the series, Square gave it's first title a bit more of a remake than in the Playstation version. Graphically, they are virtually identical, with the GBA version being a bit more brightly colored.
The big addition was the bonus area's. There is a total of four new areas to explore and conquer. Each area is accessible, once you defeat a fiend. Thus the first dungeon can be explored before you get half way through the game. Being the last title on the GBA for me to play, this was a nice thing to see. It gave the well-played game new stuff to look into early in the game.
The mode of Final fantasy Advance is the same as the Playstation's "Easy Type". The prices are reduced from the original, as well as the leveling up going faster. The caps for character levels have also been set to 99.
The biggest difference is that the MP system was placed into Final Fantasy Advance. It is presumed that this was done to make it even easier to play for the younger audience of the GBA.
Even into it's third release, Final fantasy still remains a great game. The additional dungeons provide good challenge, and the game is always fun. I would suggest for more hardened veterans to pick up the Playstation version, or better yet the Nintendo version if you can find it. This will give you the more difficult challenge of the original release. But for those who have, and are just looking to journey back to yesteryear, this is a great one to get.