Also known as "that game before Secret of Mana". It'll be out on Vita, Android, and iOS this Winter in Japan. I'm hoping this game makes it overseas as I've heard good things about the original. Besides, it's where the Mana series all started.
The graphics make me think a little of Final Fantasy Echoes of Time and Ring of Fates, as well as the chibi style of Bravely Default
Pretty sure everyone agreed Sword of Mana was awful(I played part of it on emulator and didn't think it was memorable) and Sword of Mana changed pretty much everything so it was never really a true remake. Also, we'd need Secret of Mana to be remade first. If only to have a voice actor say "Randi" all the time.
Sword of Mana was perfectly OK. And the biggest changes were simply there to remove the Final Fantasy coat of paint. Any other changes were there to take advantage of the extra options afforded to them by the GBA hardware. But that's not the point I was making. My point is that, or the well regarded Mana games, Seiken Densetsu III is still the only one that's never been released outside of Japan.