Aren't they the same in appearance? Though I will admit those two incarnations could easily have different abilities from each other (even if they don't give YL his mask transformations; on the other hand, maybe he could have still incorporated a Mask mechanic similar to Shulk's Monado Arts (for example, YL could equip a Bomb Mask that causes an explosion around him whenever he's attacked, or a Stone Mask that makes him invisible even to homing projectiles like Samus's missiles)?).
The basic design for Young Link in Majora's Mask is the same (though his artwork seems less 'childish' in MM (I can't quite explain it..I think its the cheeks?) but his gear is all different from how it looks in Ocarina of Time..and, in most cases, are incarnations Young Link can actually canonically use, since he can not use the Bow & Hookshot in Ocarina of Time..so it would make more sense that he now can use them in Super Smash Bros.
To show what I mean, I'll depict the differences between the Kokiri Swords, Deku Shield & Hero's Shield, Fairy Bow & Hero's Bow, I'll also include the upgrades to the MM Kokiri Sword, the Razor Sword and the Gilded Sword, either of which could be used to give Young Link more distinctness and if the Gilded Sword was chosen, he would then be in league with Link & Toon Link by having his Ultimate Sword instead of his Starter Sword like he currently.
Majora's Mask doesn't have a Boomerang, so that one could either stay the one from Ocarina of Time or be replaced by an item used in Majora's Mask such as the Deku Nut or maybe a spinning move utilizing the Great Fairy Sword.
I wasn't really meaning altering his moveset when I said I wanted him to depict Majora's Mask, just that I feel they should have given Young Link his Majora's Mask appearance for his equipment since its the game he's actually the primary Link of. They could retool his Final Smash to have him don the Fierce Deity Mask prior to performing the Triforce Slash just to make it a little more unique from Toon Link's, even if it would still be functionally the same.