“Liar,” Arya said. Her hand clenched the blood orange so hard that red juice oozed between her fingers.
“Go ahead, call me all the names you want,” Sansa said airily. “You won’t dare when I’m married to Joffrey. You’ll have to bow to me and call me Your Grace.” She shrieked as Arya flung the orange across the table. It caught her in the middle of the forehead with a wet squish and plopped down into her lap.
“You have juice on your face, Your Grace,” Arya said. -- Sansa III, AGOT
I really do think this interaction is setting up the ironic ending of Arya becoming a queen or leader while Sansa (if she survives), remains a generic lady who doesn't wield direct power.
In the scene, Arya is wanting justice against murderers (Jaime and the Hound) while Sansa is defending those criminals and victim blaming Mycah for his own maiming and murder. So right off the bat, it's clear that Arya is the right person to be in a position of power while Sansa needs to be as far from political and legal influence as possible. Yet, Sansa is betrothed to the crown prince and seems to be on her way to becoming queen consort, or the supposed softer, generous, and merciful face of monarchy -- a role she couldn't be less qualified for.
So GRRM is having her rub her supposed future position in Arya's face and bragging about how she'll force her into submission to set up a complete turnabout for the end of the series. In the endgame, Arya will have earned the higher place in the surviving world's hierarchy. The difference is that, while Arya often takes a natural leadership role in the groups she's in, she doesn't drool over the idea of others prostrating themselves before her the way Sansa does. So Arya wouldn't gloat over her sister, though she would continue being honest and calling out wrong doing.
Also, it's not a coincidence that Arya's direwolf is a leader and actually named for a ruling princess while Sansa's is a dead lady.