If Arya and Daenerys meet how do you think they will?

Its hard to say. I think Book Arya and Dany would get along better then Show Arya and Dany.

In the books, both young women have grown more, theres greater character development. And while the characters are canonly younger in the books vs show, I head canon that both are young women grown by the time both of them see westeros, Arya having spent a number of years with the Faceless Men, and Dany taking time to quell further rebellion in Slaver's Bay, and learn more about her original homeland from the likes of Tyrion and the Spider.
Theres also the fact that Arya spends more time exploring her Warg powers in the books then in the show. In fact, as far as I can remember, she never explores said powers in the show. Realisticly, I think Arya would need to see that she still has family left to fight for, in order for her to leave the house of black and white. Because Arya in the house of black and white is No One, No one has no family, No one has no future, no home, no hope, no love. After years as a Faceless Man, I dont see vengence as being Arya's sole motivator, let alone enough alone to make her betray the Faceless Men and leave the way she did in the show.

And Book Dany was a bit more mature, had a bit more grace, and while jaded as fuck, wasnt exactly as luke warm as she is in the show when it comes to matters of the heart. And, in the books, she was and is way more bisexual. Which is always a plus. I also cant see her leaving slaver's bay without securing her power base there once and for all. It would be foolish and short sighted of her. Her journey from sheltered princess, across the grass sea and red waste to Quarth, then beyond to Slaver's Bay would have taught her more, taught her better. This is a young woman who genuinely cares about and for her people, and she'd know that to leave without securing her rule, securing her power base, would leave a void and the people she freed, those who call her "mother" would suffer the most if she goes to westeros without doing so. So again, it would be years.

In the show? Neither young woman are quiet right for eachother, they dont have the years, the experiences. Arya doesnt have her abilities, doesnt have that connection to home beyond her desire for blood. And Dany hasnt truely figured out how to lead. Yes, shes queen, hell, shes practically a empress, but she hasnt learned to lead yet. And while she cares about her people, she hasnt learned how to take care OF her people. Shes still to much of a pawn to be a player of the game.

I think at their core, they'd get along, that eventually they'd trust eachother. Arya would be the first to see past the histories of their families, be the first to push beyond the grudges of their parents and older siblings. Her obession with dragons would help in that reguard. But it would be Dany that would reteach Arya how to be human, to be SOMEONE instead of No One.

I could literally right a essay on this, I could, but I'm not going to.

The show did a few things right. One of them is it aged up the characters by a few years compared to the books. (Arya was 9 in Book1, but 11 in S1 I believe) The show also gave us clear faces, heights and voices for the characters. Which does make things a bit easier. I personally can no longer picture Tyrion as anyone else other then Peter Dinklage, which isnt a bad thing, at least for me it isnt.

Of course, my own story, Frosted Faith, is a AU, where the Starks never left the North, and as a result, things have move slower, and events happened much later. So all the characters are older. I'm also bringing in elements of the Tall Tale game for added flavor.

I think over all, when it comes to canon, and show vs books, you have to make up your own mind. Researching lore helps, going back and re-reading or re-watching this part or that scene is also always good too. More so since the show is radically different from the books at this point in time.

I think depending on where in the time line your story takes place, you'll have a Dany who is slow to trust, and a Arya who is quick to anger, and theres a lot in just those two traits that you can work with to create interpersonal conflict. But the key factor with both these characters is remembering who they are at the core, which means looking back to their S1/B1 selves. And finding the things they have in common.

My personally fantasy is that the first time Arya sees Daenerys, Dany will have landed on Drogon and Arya sees her for the first time on the dragon.
This is probably not going to happen by any means but a girl can dream.

i am thinking they are going to meet in the north before they ride off to war... i really hope one of the stark kids wargs into a dragon. i hope they get along and she doesn't murder tyrion cuz that wouldn't make a good first impression

Huh, random thought. Arya knew his dad.  I don’t think any other Stark child did (could be wrong). They could bond of what an asshole but also truly cunning man he was. Also, does everyone know Tyrion didn’t kill Joffrey? Because Arya might shake his hand for that. 

I would have been interesting if Dany had seen Lyanna as part of her visions of Rhaegar. I believe Arya has been told she reminds people of Lyanna so it would be interesting if Dany had already recognized her somewhat (unless I'm remembering this comparison for Arya from something else).

I could just imagine the scenarios from people that join Dany in canon and are introduced to a painting of their future queen. The reactions of Tyrion and Theon being shown it would be funny. Not to mention if this picture gets spread to Westeros before Dany gets there so you could see how Cersei or the Hound react.