I have Final Fantasy 1 for my Nokia, and it's actually a port rather than an emulation. I haven't looked up the differences, but what I've found so far are:
The interface supports tapping on characters rather than selecting them with the 'directional-pad' which appears on the map when walking around.
There's at least one new area to explore.
The magic system is more like later games, using MP.
Graphics have been improved
I'm not sure how many of these are ports from the DS version, though. Possibly all of them.
Based on the screenshots of FF3 for Windows, it appears to be a port of the DS re-make rather than the Famicom original
I think they're mostly just ported. I've bought a few of the Square games on iOS and they were just the normal games with touch capabilities added on top of the old menus. No usability changes at all to accomodate modern touch patterns. There are many "click" needed to navigate some menus, which would just have been one touch or drag in a modern app. Scrolling was also laggy and glitchy.
I'm not sure how many of these are ports from the DS version, though. Possibly all of them.
Based on the screenshots of FF3 for Windows, it appears to be a port of the DS re-make rather than the Famicom original