I'm going to challenge that, BJN39.
In Melee classic it's amazing to be below Zelda because she has nothing there. She's floaty and has no real threat.
In SD Remix in addition to better physics (her aerial momentum control looks better - not sure if this is a byproduct of other buffs or if they actually buffed that specifically), faster jump speed, and quicker ground mobility she also has Ganon's dair.
This Zelda basically looks like if you combined Ganon with Puff and tossed in Peach's dash attack for posterity's sake. This looks NOTHING like Melee Zelda.
I mean, she looks like a fun character to play and all. But she doesn't look anything like her Melee counterpart. The fact that she's jumping (full jumping, for that matter) as her primary means to approach, defend, etc. is indicative enough. Modern Zelda is primarily a ground character (unless you're Cosmo basically [and even then I kind of think his air style was the byproduct of living vs so many defensive players]). Even then, Cosmo still understood the merits of ground and played somewhat close to it for the most part with SHs. FJ viability and massive mobility enhancements and the presence of a threat underneath her are big changes.
That said, she looks sort of fun to play.
edit: I also think I saw Nayru's knock down at 0. Not sure if it does that in Melee classic but it looked odd. Tempted to check but kind of lazy too.