GameXplain just released a bunch of videos about stages so I'll share my thoughts:
Orbital Gate: Well it looks beautiful but the transitions are extremely quick, to the point where I worry if there'll be lots of SD's moving to the new platforms. You spend all of like 10 seconds on the Great Fox. :/ Also lasers flying around randomly, not sure if they damage you though. I'll need to play this for myself.
Wooly World: Walk off>Interesting Platform Placement>JK BACK TO WALK OFF. It'll be okay in casual play.
Kalos League: The Water section isn't a big deal. The rushing water comes down once and quickly, though the walk-off sections are there for the entirety of the water section. Spends about 20 seconds or so in each section. Swords in the steel section are solid objects with hitboxes though. No word on fire or dragon. Considering the swords don't let you pass though I doubt the fire will and rayquaza is probably a boss. If so, stage is dead. If not, this could be okay in casual play, but the solid swords kill any chance of competitive play it had.
Mario Circuit: Not bad, there is one stop on the track with a walkoff on the right, and one stop in which 3 drivers go through the center of the platform. I'll enjoy this stage, and it has a chance for counterpick status.
Jungle Hijinx: The center of the foreground platform can crumble Green Hill Zone style, but comes back up relatively quickly. There's also the tiki tower thing, but that's not in this video. This stage will be fun to play in FFA's, I think I can even call this a good stage.
Wrecking Crew: It's...surprisingly playable. The bombs don't collapse the platforms, rather they open up pathways through the existing platform setup. I need to play this for myself to judge further.
Great Cave Offensive: lol that camera. I have no idea what to think of this, but hopefully it's fun with 8 players.
Hopefully Pilotwings is next, as that looks like the best stage in the game IMO.
Edit: Apparently Pyrosphere and Wuhu Island were next, so I'll just update this post accordingly.
Pyrosphere: Well it's what you'd expect. Enemies randomly fall down and Ridley comes out after about 30ish seconds? It might be fun in casual play, idk.
Wuhu Island: GOOD STAGE, WE HAVE A GOOD STAGE. 2 walk off sections, but for the most part, this stage looks fantastic. Definite counterpick contender.