I wrote something about its story there :
http://sumarucity.com/megami/yabb/YaBB.pl?num=1201190215 .
I've only played the SNES Kyuuyaku version, but judging by the gameplay videos on Nicovideo and the few things i've been able to translate from japanese walkthroughs almost nothing was changed.
The first one is quite a nightmare to play through. The giant dungeon can get very boring at times, especially with the lack of Estma, there is very little to actually do, as you'll need so much backtracking for every single quest that you'll probably end up overpowered through grinding anyway, and
THE MONSTERS ARE DULL ! even though this is a SMT title ! There are too many palette/head swaps, too few different abilities and even the designs are not up to par (especially in the NES version).
The second, on the other hand, is almost as good as the first Shin. It adds a map, with many smaller and more reasonable dungeons, 3-monster fusion (and an unnecessarily complex sistem of Seirei, with 12 members ), better and more varied monsters and abilities, and a story with some two-way choices (pity i'll not be able to actually confirm anything about what changes, having lost my saves JUST BEFORE FIGHTING THE USUAL MR.FLOATINGFACE !).
Overall, a very good game.