Graphically, Origins is different. Aside from that they're exactly the same game save for a few tiles' worth of terrain in some of the dungeons where bosses are placed. But then again, that's graphically. So yeah. They're the same game as long as you play on normal mode.

Wait, gameplay-wise I can think of a few minor things:
-The Mythril Sword (SILVER in the NES version) is not available in Elfland
-Items. You can have as much equipment as you want, and anybody can use the items in battle
-Chaos has more HP, but you guys touched on that already