See, Wuthering Heights is about a woman, Catherine, and her sort-of "foster brother", Heathcliff. The two of them, as nearly as I can make out from the first half of the book, are complete reprobates with barely a redeeming quality between them. For cotnrast, the book has another brother-and-sister pair, Edgar and Isabella. The latter two are ordinary, respectable people who are apparently otherwise quite likeable apart from being dumb enough to marry, respectively, Catherine and Heathcliff. Who then go on to destroy their spouses' lives as well as their own.
Mansfield Park, by contrast, tells the story of a young man and his "poor female relation" (cousin, if I recall correctly) who grows up with him. These two are pleasant, respectable characters. Over the course of the book, they are courted assiduously by a brother-sister team of questionable morals and motives. There's some question as to whether the first pair might actually be able to instill some goodness in the latter. But by the end of the book, the reprobates have shown their true colors, and the man and his cousin turn them down and marry each other instead.
It's almost as though Jane Austen had read Wuthering Heights, thought "This is dreadful! It's a pity Edgar and Isabella couldn't marry each other, they'd've been much better off" and then set out to write just that novel. Of course, this theory was much more interesting before I checked the publication date on Wuthering Heights -- 1847, well after Austen's death and 33 years after the publication of Mansfield Park.
I imagine Brontë could've been inspired by Mansfield Park, along the lines of "What a dreary respectable happy ending! Wouldn't this've been a much better book if they'd married the reprobates and been dragged through the mud, tortured, and ultimately died miserable tragic deaths? Yeah, I'll write that!"
It's probably worth noting that the reprobate couple from Mansfield Park, who are side characters in the story, nonetheless manage to be more likeable than Brontë's protagonists. It's difficult to tell the life stories of characters without making them seem somewhat sympathetic, but Brontë's really doing a bang up job of it so far. I admit I'm only halfway through, and there's definitely some question as to narrator reliability. Maybe some glimmer of likeability will yet emerge for the protagonists, but I'm not counting on it.
One of the reasons I initially thought of Austen being inspired to write the anti-Wuthering Heights is that one of her other novels, Northanger Abbey, clearly was inspired as a reaction to the melodramatic, overwrought and implausible fiction of her day. Northanger Abbey is full of references to melodramatic novels, which are a favorite pastime of the protagonist and most of the likeable characters in the novel. And it goes on to poke gentle fun at the tropes of melodrama by having absolutely none of them take place. Austen's books are, in general, quite grounded in reality. Paupers do not turn into instant heiresses by being found by their long-lost relations, husbands do not drive their wives to insanity and then kill them, women do not dissolve into fits of passion and die because their best friends get into arguments with their husbands, etc. The most unlikely thing that ever happens in an Austen novel is that rich men occasionally fall in love with and marry genteel but impoverished young women.
I think it's clear that Austen really enjoyed the outrageous and impossible tales that she refers to in Northanger Abbey. She writes of them with loving affection, as harmless diversions, providing little substance but much entertainment. But I don't know that she gets nearly enough credit for not writing such fluffy fantasies herself.