Something which constantly baffles me is why so many people sort Sansa into Ravenclaw and Arya into Slytherin – because canonically, personality wise, this should be the complete other way round.
Sansa is cunning, ambitious, resourceful, determined.
She survives King’s Landing by being completely out in the open, and therefore nobody suspects her of ever trying to do anything questionable – because she always has eyes on her (or so it is believed), and she so frequently states her love for Joffrey, everybody believes she is who she presents herself to be. That is cunning.
She held the aspiration of wanting to be Queen, alongside Joffrey, thinking how this means she could finally put Arya in her place – and now is aspiring towards being Lady of the Vale, and it is implied, through Littlefinger, the end goal is to have her crowned as Queen in the North. That is ambitious.
She knows the society that she is in, and knows the rules and regulations, and uses this to her advantage. She gets people on her side by being the epitome of a well behaved lady, and knows the value of her beauty and her behaviour. She then turns this on its head to make her the one in power, her the one in control, and it elevates her out of the diabolical situations she is forced into. She uses the system she has available, and she plays it. That is resourceful.
She is constantly wanting to get home to Winterfell, and everything she does is to aid that in the long run. The Vale is a safe place for her, but she has not forgotten what she is there for. She is there to eventually get home to Winterfell. All of the previous actions stated, actions which are cunning, ambitious, and resourceful, are underpinned by unwavering determination to get home.
Arya, on the other hand, is intelligent, witty, creative, accepting.
She speaks several languages by the time we reach ADWD, is good at mathematics, has a vast knowledge of Westeros’ history and constantly wants to know more, not only understands the societal system she is in but also questions it, knows how to lie and manipulate situations to her advantage, has knowledge of plants and can tell direction from them, and is very intuitive, sensing that they should go far before Yoren sounds the alarm in ACOK. This shows deep intelligence.
She gives as good as she gets, regardless of class – jibing with Jon right from the off, hitting Gendry and arguing with him (with no small dash of intellect), when Lommy is going on and on about yielding and they leave him to check the path ahead and he asks “What if the wolves come?” she wittily, to mock him, responds, “Yield.”, gets hit by a range of people for her inability to hold her tongue, because if Arya sees a situation she can be witty and sharp in, she generally always is. This shows she is witty.
Arya is confronted with a huge range of situations to struggle through in the books – and she deals with them in a number of different ways. From talking her way out of a situation, to using Jaqen H’gar, to straight up killing people herself, to learning how to play the game of Faces, to gaining comfort through warging as Nymeria; Arya shows she has a huge breadth of creativity with facing these problems.
She also speaks with everyone, and gets on with and makes friends with everyone, regardless of their class. In fact, class is rather irrelevant to Arya. She never refers to Jon as anything less than her brother; he is a bastard, and she knows this is a big deal in society, but to her it is not, because she is simply her brother, whom she loves. This shows she is accepting.
Of course, there is overlap between the two (they are, after all, sisters) – Sansa is most certainly intelligent and at times creative in the way she survives King’s Landing and onwards. Arya is most certainly resourceful and determined on her path. Sansa however, is not particularly witty, and certainly doesn’t accept everyone in the same way Arya does; and Arya meanwhile is not ambitious, and is not particularly cunning either. She has the ability to be, but does not enjoy the game in the same way Sansa does, therefore I don’t feel it counts.
TL;DR Arya is a Ravenclaw, and Sansa is a Slytherin, and there is more than enough evidence to confirm this.