Skullgirls vs Chainsaw Man

Connection:

Both are ancient, sadistic demonic antagonists of anime-esque forms of media, who have existed since the early days of human civilization (Eliza has existed since the Skullgirls verse's equivalent of Ancient Egypt, Makima as the Control Devil has existed since the first time humans feared being oppressed and controlled)

Both belong to a race of demonic beings who have existed since the beginning of humanity (Parasites and Devils), with the modern times causing a massive rise in their population in the human world, as well as their subsequent taming by human hands (Parasites often unite with humans to survive, whereas Devils form contracts with Devil hunters to exterminate other Devils)

Both sides also coincidentally have an important figure responsible for their reputation (Sekhmet is the Parasite that ruined her entire race's reputation and made humans see them as monsters, the Chainsaw Devil rescued many Devils from an unknown catastrophe in Hell by killing them and bringing them to the human world)

Both would hide themselves among the human populace, taking the guise of public workers responsible for important societal services (Eliza leads a charity blood drive, Makima works as a Public Safety Devil Hunter). These services however, are meant to hide a much more sinister truth about them that is related to preserving their bodies (The blood drive is actually a means to maintain Eliza's ageless beauty, Makima's job is the second part of her contract with the Prime Minister of Japan, which is meant to resurrect her and transfer any fatal injury onto a random Japanese citizen, keeping her from truly dying)

Both work for highly influential institutions in their settings (The Medici mafia and the Japanese government respectively), and are even said to have unwillingly become their workers (Eliza is under threat of being exposed as the monster she is unless she cooperates with the Medici, Makima is theorized to have been molded by the government into what she is now)

Both fight with the aid of supernatural hybrid helpers (Eliza's henchmen, Albus and Horace, who are ferals (half-human, half animal) and Makima's Fiends, which are Devils inhabiting human corpses), and who either serve them willingly (Albus and Horace), or were forcefully enslaved by them (the Fiends)

Both have taken a huge interest in the protagonist, mostly due to the fact that said protagonist has a particular being of great interest to them attached to their bodies (Filia, who is the host of the hair Parasite Samson, and Denji, the host of Pochita, the Chainsaw Devil). To this end, both would go to great lengths to utterly destroy the protagonist so they could get their beloved demon all to themselves (In her story mode, Eliza enslaved Filia and plans to find a more suitable host for Samson before disposing of Filia. Makima manipulated and built Denji before tearing him down in an effort to make him fully surrender to her and grant her control over the Chainsaw Devil)

Both are so obsessed with their demonic interest, that they went so far as to personally murder their closest friends right before their very eyes (Eliza killed Samson's oldest and most beloved host, Delilah, so she could forcefully take him, while Makima killed Denji's closest friend Power while making him watch, in an effort to utterly and completely break him)

Both hold special titles that betray their true nature and speak volumes of the horrible things they've done (The Crimson Scourge and The Control Devil respectively)

Both hold a disdain for the current state of their societies, and desire to rise in power in order to change them in their ideal image (Eliza wants to conquer the world and shape all of society into her ideal image under her rule, while Makima wants to use the Chainsaw Devil to erase any and all bad things that exist in society)

And yet, despite all the horrible things they've done, every last drop of blood they've spilled, and every last person they've killed, both still have an inner desire that is ultimately good and benevolent in nature (Eliza wants to bring the entire Parasite race to it's former glory and save it from extinction, Makima desires to live a happy human life with a family she doesn't control and loves unconditionally)

The contrast is that Eliza is a fan of cats, whereas Makima is a fan of dogs