Whitebeard and Big Mom are both very old Emperors that few would want to cross but they have virtually opposite standards.
Whitebeard felt every pirate should have a code and sense of honor. Big Mom lies and regularly deceives and tricks others to obtain her own ends.
Whitebeard never had any actual family (his alleged wife and son notwithstanding), but he treated every subordinate as if they were one of his own children, forgiving one for stabbing him, and he led them with sincere, if gruff, love.
Big Mom’s children are related to her by blood, yet she feels no true love or compassion for them, treating them as no more than a means to an end, and killing them if they go against her.
Whitebeard protected Fishman Island and demanded absolutely nothing in return for his protection. Big Mom not only made a massive demand for candy from Fishman Island under her protection, but she was highly inflexible about receiving her payment, and it’s only thanks to Luffy that she didn’t unleash her wrath upon the island.
While Big Mom is leading her crew by fear (which she invoked so that she could take their soul away), Whitebeard led by love.
Big Mom imposes her will on her kids and as well as her allies. It was not the case with Whitebeard, he never imposed his will on his allies and even his crewmates. His tag line was “Bear my name on the back and roam the sea freely” while Big Mom’s tagline is “You can only leave Totto Land after your death”. Whitebeard didn’t discriminate anyone on looks but Big Mom discriminated Pudding and Katakuri.
Even the contrast of their powers is interesting as Whitebeard could control the land and sea with his powers (quake) while Big Mom’s powers (soul) she uses to manipulate something that represent the sun and sky.
Both of them suffer from a form of illness which hurts them: Whitebeard a physical illness which led his body to be weakened and left openings for people to attack while Big Mom suffers from a mental illlness which occasionally activates (her hunger pains) and can lead her to cause damage to her own crew and lands.
*Theory by kingace22
