The SNES version had the ability to save which really should have already been there for a game the size of SMB3. And I like how the SNES version doesn't **** around with the game itself. It adds the save, improves the graphics and sound and that's it. Otherwise it's the same game.
I think it benefits from the time it was released. SMB3 was not that old of a title yet so the game design conventions of the day were similar. These days things have changed too much. A lot of the game design conventions of the NES era are, right or wrong, regarded as out-of-date by developers. So there is a tendency with remakes to modernize the game for the current audience. But since these games weren't designed with those modern changes in mind the balance of a game can be thrown out of whack.
Plus Nintendo put Mario's voice in the remake.
To me an ideal remake should only try to patch up the rough stuff. Tighten the controls if they're loose, add save capability, fix bugs, bring graphics and sounds to a level where it isn't hard to look at or hear them, boost clunky framerates. And then there's also stuff like streamlining the menu in Dragon Quest or making it so you don't attack dead enemies in Final Fantasy. The goal should be to try to present as close to the same game as possible, just without the broken stuff we no longer will tolerate. It's more like just making the game available on modern systems.
Or the other option is to go all Metroid: Zero Mission where the remake is so different that it's really a brand new game that's merely inspired by the original. That's more like a movie remake where it's the same general plot and idea but with a different director, script and cast. Either go for broke or be conservative. Don't do this in-between bullshit where you just end up breaking the game.