Whose story is it: Hester's or Dimmesdale's? and why?

I think you could reasonalbe argue for either one.

It is Dimmesdale's and his puritan society that the whole story revolves around.

His failure to concede to his natural feelings harms everyone he is near to, yes! including Roger Chillingworth! How far could Chillingworth torture Dimmesdale if he was not a prisoner of his own beliefs! You can only feel shame. only feel insecurity and only feel mentally helpless, if you allow yourself to be so.

By not relinquishing his prestigious position in his society, he allowed all around him to suffer along with himself. He could have changed everything by admitting his errors and start up a new life elsewhere. Hester carried his shame in The Scarlett Letter and that only served to increase his masochistic tendencies and torture more so. The fact that he tried to redeem himself when it was too late and he was dying provokes the question: Why not sooner, and live a happy life?

We must remember that Hawthorne was probably trying to show the weaknessess of his puritanical background, a subject he touches on in his other short stories, such as "The Minister's Black Veil".