If we're talking about story, meaning the why and the tone, the character journeys, I'd probably put 4 and 6 on the pedestal, with 13, 10, and 7 as the next tier.
FF4's story is relatively simple, being first about redemption of a tarnished soul, and then the attempt to bring about the redemption of others. And all of this is housed in a very simple fantasy setting, with many of the tropes of the genre. But I'd actually argue that no other FF game has such a strong undercurrent of meaning from start to finish. Final Fantasy IV is about saving your soul, and then saving the souls of others.
FF6, in my opinion, has the best PLOT of all the FF games. <Sorry, had to cut most of the content I'd originally posted here - I've found my next editorial!> At any rate, it doesn't have the true overall tone that some of the FF games had, but it had more characters, and more quality of storyline for each character, than many of the other games I've played. If you could even drag out the depth for these characters more, it would be even better - but what this game lacks in depth, it makes up for in breadth.
I still (firmly) believe that PS3-quality remakes of 4, 6, and 7, using the Crystal Tools engine, and slightly revised battle systems, would be among the greatest games ever built. I bet they'd sell well too.