What they changed
3d Graphics/Theoretically HD (The art style doesn't make use of the HD at all) - Generally this doesn't affect anything. The cutscenes with camera angles manage to look kind of awkward a lot because they did stick rigidly to the 2d designed environments so you get some oddities in the background that don't work out.
Added voice acting - Opinion may vary, but much of it sounds incredibly stilted. They're reading clipped lines that had to be written to fit on a SNES with no alterations after all. The new conversations in the Inn feel slightly more natural, but they're written in that awkward "Adult tries to write teenagers and makes them sound like they're 12 even though they're clearly older" style. Secret of Mana's minimal characterization to begin with did have some of the same effect, but it was smaller and didn't raise questions of how these goofy immature kids would manage to do the serious stuff they start doing.
Gameplay:
Fun thing about 2d sprites, its pretty easy to make hitboxes for them. 3d sprites not so much apparently. You'll get more then a few cases of wonkiness. Not to worry though, because they seem to have anticipated this situation, and half the weapons or so have had their hitboxes doubled or even quintupled (seriously, check out the sword swing arc between SNES and the new one, lol). So melee combat became a ton easier (whether thats a good or bad is up to you)
Enemy spells . Getting blasted by enemy magic or seeing cures land on the thing you're fighting is annoying, better go kill that pesky mage, right? In SNES SoM enemies blinked when they were casting one of the spells, which otherwise materializes out of nowhere. They apparently decided that was an undesired artefact or something, but never bothered adding an animation or anything for it. So now you get to play guess which enemy (including potentially offscreen ones) is casting stuff at you.
Archer type enemies that you could dodge around in the original because they shot in cardinal directions will now happily fire arrows directly at you at any angle. Since they gave you the same freedom, it'd be cheesy if they couldn't. But since hits can stunlock you, have fun with group situations. Its nit picking perhaps, but more signs of how lazy they were in making decisions.
Some general jank they decided to leave in. Since they went shot for shot (literally they use the SNES map as the minimap, a cute nod, but also kind of telling to how little they changed anything that it works), areas are *tiny*, and there's still a transitional loading delay between them that has no real reason to be there. Similarly in combat, damage numbers are on a true-to-the-original, but baffling 2-3 second delay.
The Real Kicker:
If you're familiar with the vidya game history. You might know that Secret of Mana was a title slated for the Nintendo/Sony collaboration CD system. Now that didn't work out, and Secret of Mana would be ported to SNES cartidge instead. Mana had enough unique qualities for the time to carry itself, but you can start seeing the cutting room marks from the stripdown when you look at it in any detail. Missing weapon upgrades, reused enemies all over, single room dungeons or bosses awkwardly dumped in (Immediately after you meet Thanatos and fight the Wall boss, there's a sequence of sudden boss rush, for instance, where you fight five bosses in a row out of nowhere). Even several gaps where the story just vanishes until you figure out where to go on your own, seemingly because a scene or encounter got pulled that would've told you to go somewhere.
So Secret of Mana, a game that more then almost any other thats gotten the treatment, man, that could really use a remake to iron out those problems and present the game in its original intended format....
But nope. Instead they went shot for shot, without a lick of actual added content other then the inn conversations. Its not like they'd be writing fanfiction into it either, its the same company that made the original and would have the information available to them on what they made.