I'd have to say that Battlefield is the most balanced stage. The ledges don't prevent any characters from recovering. Three platforms that are all equal in length. A nice sized base platform. It gives every character an advantage and disadvantage.
FD is too large and, as mentioned before, the ledges prevent some character recoveries. Plus, the stage being flat gives projectile characters a higher advantage, as well as giving runners a larger area to escape on. SV would be the best, if the platform didn't move. The moving platform adds a variable to the stage removing part of its neutrality factor. YI has the ghost platform, the center platform moves occasionally, and the ledges on the stage can hinder a few characters recoveries. LC tilts and hinders some projectiles, not to mention the background is very distracting and the ledges can cause some characters to get stuck under them.
After considering all these factors, the only downside to BF would have to be the platforms, but they are better off than SV's platform because they are stationary. So yes, IMO, BF would have to be the best andd most fair stage. Then again, it's just my opinion.