wow... last time i played a good mario... is a long time ago, poor underrated character
well lets seee i'll try my best to break it down with what i know...
the fludd isn't so good... but its enough to push sheik away from the ledge where as zelda can FW back to the stage from far away outside of the range of FLUDD and a potential cape, even though mario does have that cape off the ledge technique which is fun to do
mario has some crazy juggles and since zelda seems to be floatier she can get out of them easier even though she's heavier... makes no sense to me but it seems to work seeing how sheik gets CG easier while zelda escapes most of the CGs out there.
mario can be combo-ed prettty easily by sheiks ftilt, but at the same time since mario has pretty poor range on his moves due to his stubby legs and arms zelda will have no problem landing her moves on him as well, only difficulty would be the lightning kick but you just need to aim low and if you haven't perfected that then... this thread is ... kinda not for you now is it.
as for an aerial battle, it seems like if sheik is under or at the same level as him then she has the advantage while if she is above him she is at a disadvantage, we already know zelda isn't that great from being attacked anywhere from underneath, the vulnerable under belly :]
dins will work very well on mario, if he tries to cape it you can simply make dins move behind him and hit him while his cape is out... the cape will probably get him more hurt than an aerial dodge or a roll/spot dodge
mario's fireball is mediocre but it can be effective against a sheik, but so can sheik's needles be effective on a mario so ... just cross that out
over all... since mario isn't that fast nor heavy zelda will have an easier time in killing him it seems where zelda can be either aggressive or defensive, its up to the zelda player
sheik will do well in being aggressive where sheik can try to gimp mario's recovery, since the fair and nair come out faster than marios fair and marios nair has quite little range it'll do well to gimp where the cape could turn sheik around but chances are a nair will hit him as well as turn sheik around toward the stage and help her...
all in a hypothetical situation, zelda