The vast difference in how Jon Snow deals with the marriages of Arya and Sansa Stark has already been mentioned. However, I noticed there are also other differences in the overall narrative as well.
First, two Kings - Robb Stark and Stannis Baratheon - refer to and use Sansa’s marriage to Tyrion to affirm that Sansa will never get Winterfell while positing that Jon Snow should be Lord of Winterfell.
“Young, and a king,” he said. “A king must have an heir. If I should die in my next battle, the kingdom must not die with me. By law Sansa is next in line of succession, so Winterfell and the north would pass to her.” His mouth tightened. “To her, and her lord husband. Tyrion Lannister. I cannot allow that. I will not allow that. That dwarf must never have the north.” - Robb Stark, ASoS
“By right Winterfell should go to my sister Sansa.”
“Lady Lannister, you mean? Are you so eager to see the Imp perched on your father’s seat? I promise you, that will not happen whilst I live, Lord Snow.” - Stannis Baratheon, ADwD
In contrast, two Kings - Mance Rayder and Stannis Baratheon - are trying to save Arya Stark from her marriage to Ramsay Bolton for Jon Snow.
He glanced at the letter again. I will save your sister if I can. A surprisingly tender sentiment from Stannis - Jon, ADwD
Bring her home, Mance. I saved your son from Melisandre, and now I am about to save four thousand of your free folk. You owe me this one little girl. - Jon, ADwD
It’s interesting that Stannis has this ‘tender sentiment’ while vowing that Sansa will never get Winterfell considering that Arya too is married to his enemy Ramsay Bolton. Maybe he intends for Ramsay Bolton to be dead soon which would free Arya to make other alliances. Or maybe he hates the Lannisters more than the Boltons.
Additionally there is no other mention of the Sansa/Tyrion marriage in the Northern context, no Northern houses or lords who bring it up, no secret plotting that revolves around this marriage. In contrast Arya’s marriage to Ramsay is mentioned in the four corners of the North, from the Wall to Winterfell, from Deepwood Motte to White Harbor and is a driving force for many of the characters’ actions and plotting. It’s more important in terms of ‘The North Remembers’ and Northern uprising against the Lannisters in King’s Landing, the Freys and the Boltons considering it revolves around Lady Arya Stark present in Winterfell.
This is why - as GRRM has pointed out in interviews - Arya’s marriage to Ramsay is a necessary and important book plot.
Unintentionally. A little change in a long narrative can have big changes further on. You know, when we remove Jeyne Poole from season one, then you don’t have Jeyne Poole to be the fake Arya, as happens in the book. So what do you do then? The butterfly effect has done that.
It’s not Jeyne Poole’s marriage to Ramsay Bolton that is driving all these mini subplots in the North.Yes, it’s sad that no one would care if Ramsay married Jeyne just like no one cared that Jeyne got send off to the brothels while Sansa was a high value hostage of the Lannisters. Just like no one cared about Jeyne’s story in the books until the show replaced her with Sansa and suddenly there were discussions about rape in the series.
GRRM: I was trying to set up Jeyne for her future role as the false Arya. The real Arya has escaped and is presumed dead. But this girl has been in Littlefinger’s control for years, and he’s been training her. She knows Winterfell, has the proper northern accent, and can pose as Arya. Who the hell knows what a little girl you met two years ago looks like? When your a lord visiting Winterfell, are you going to pay attention to the little kids running around? So she can pull off the impersonation. Not having Jeyne, they used Sansa for that. Is that better or worse? You can make your decision there. Oddly, I never got pushback for that in the book because nobody cared about Jeyne Poole that much. They care about Sansa.
In the books, it’s Arya marriage that has two kings trying to save her, the Lord Commander of the Night’s Watch breaking sworn oaths, the Mountain clans and Northern houses marching with Stannis for the Ned’s precious little girl. They all think that’s Arya Stark in Winterfell. Arya may not be physically there, but it’s the marriage of Arya Stark in Winterfell in front of the Heart Tree, being given away by kin, Theon Greyjoy, that’s being used to hold the North and lend legitimacy to Ramsay Bolton as Lord of Winterfell.