The other stories lost the popularity contest for various reasons. Bluebeard had a decent chance thanks to the sway of being the best-known version, to the point the story archetype is named after it, but Perrault's hamfisted and sexist moral at the end robbed it of its chances. Besides that, the main character lacked any real initiative. While she did discover the fate of the previous brides, she depended on her brothers to save her without any real action on her part besides sending someone for help. The Robber Bridegroom was better, but the main character also ignored several major hints that there was something wrong with her husband, including outright verbal warnings from wildlife. Fitcher's Bird came the closest, as it involved cunning on the part of the protagonist in multiple parts, but Mr. Fox won out for me because of its presentation.
A common part of all these stories is the death of the Bluebeard character. In Bluebeard this occurs when the protagonist's brothers arrive and kill him, in Fitcher's Bird it's when he's trapped and burned in what he thought to be a wedding reception, and in The Robber Bridegroom it's when he's captured and executed by authorities. In Mr. Fox, it comes as a culmination of a buildup created by the protagonist. Before the wedding, she's witnessed her fiancé, Mr. Fox, carrying a dead body to his home. She'd collected a severed hand and ring from the body and prepared for the wedding the next day. There she recounted a peculiar dream she'd had, one that bore a peculiar resemblance to the scene she'd witnessed the night before. But it was only a dead, she repeated, even as she repeated "Be bold, be bold," the inscription from the archway to Mr. Fox's castle where's she'd seen it. At the climax of the tale she revealed the hand and ring, and Mr. Fox was cut down by her brothers and friends.
The heroine of this story was brave, cunning, and had a taste for theatrics. She was brave enough to uncover her husband's misdeeds, as with all the protagonists of these stories. She was cunning enough to avoid being found out and set a trap, as with the protagonists of all but Bluebeard. But only the protagonist of The Robber Bridegroom has the same type of theatrics as her, and between the two, Mr. Fox's heroine pulled it off better. She gives Mr. Fox chances to interject, where he says "It is not so, nor it was not so. And God forbid it should be so." He continues to dig his own hole of denials as she builds up to the reveal, a reveal she could have made easily at any time but decided to drive in. She wanted him to know that she knew, letting the dread build before the final reveal. It's not often that our protagonists get to pull off such smug gloating, and it's satisfying in both a narrative and a schadenfreude sense to read.