Well the origonal Final Mix only had a couple extra pieces. Namely a fight scene with Xahenort and letting you fight Sephiroth in the Collesium as you couldn't origonally in Japan. (oh and a few extra fights.) Beyond that they extended Deep Dive a tiny bit but not enough for it to make much more sense. I wouldn't get your hopes up.
Oh and KH1 Final Mix had English voice acting with Japanese Sub-titles so for the most part you can play it just fine.
There really wasn't all that much added.