Funnily enough, I am actually finding FD fine as Bowser but am struggling on Battlefield. I was considering starting a new thread but since we're talking about stages, I think the only one where he really suffers is the after mentioned.
While I found it manageable in Brawl, I've been spoiled by FG 1v1 for too long and this has pretty much made me rather helpless on Battlefield platforms as I have no idea how to utilize them effectively, especially in the new format. Ganon's side-b blasts me onto one of the lower two platforms and I eat an up-smash or vs other melee characters, they harass me with f-airs and u-airs as I desperately try to get back to ground level. As well, against ranged characters, the platforms feel like they get in the way I try to meet them back on the bottom level once more. Any advice fellow Bowsers?
As for the rest of the levels, I feel the FG/FD is fine for Bowser so long as you got your shield work down and know what the characters are capable of. Particularly vs ranged they got no where to hide and closing the distance is simply a case of blocking at the right time and knowing your spacing. That said, Prism tower I felt was quite a smooth transition for Bowser despite the changing of the level all around. That and the aftermentioned Yoshi's Island feels quite good to sneak in a few good up-smashes. I struggle though when it comes to the above mentioned BF.