How does Hester Prynne compare to the more usual women in Puritan society?

It is important, I think, to note that Hawthorne does a bit of a disservice to the Puritans by presenting them, on the whole, as a pretty awful group of people. To be sure, they absolutely had their flaws, but they also had their good points, though he—for purposes revealed by the narrative— paints them in an especially negative light. That being said, almost our first introduction to Puritan women is that

Morally, as well as materially, there was a coarser fibre in those wives and maidens of old English birth and breeding than in their fair descendants, separated from them by a series of six or seven generations [....]. The bright more sun [...] shone on broad shoulders and well-developed busts, and on round and ruddy cheeks, that had ripened in the far-off island, and had hardly yet grown paler or thinner in the atmosphere of New England. There was, moreover, a boldness and rotundity of speech among these matrons [...] that would startle us at the present day [...].

Thus, the Puritan women are described as rather beefy and tough, both physically and emotionally. They are large and loud here, not fine and fair as their descendants grew to be, after several generations of living in Massachusetts. These women are also very judgmental and unforgiving, talking about the punishments they would inflict on Hester Prynne, were it up to them. One would brand the "A" on her forehead, while another would see her dead.
Hester, on the other hand, is almost the complete opposite. She

was tall, with a figure of perfect elegance on a large scale. She had dark and abundant hair, so glossy that it threw off the sunshine with a gleam; and a face which, besides being beautiful from regularity of feature and richness of complexion, had the impressiveness belonging to a marked brow and deep black eyes. She was ladylike, too, [...] characterized by a certain state and dignity [...].

Physically, then, Hester possesses a grace and dignity that her peers in the community do not seem to have. She is also beautiful and delicate, where they are ruddy and robust. Further, she conducts herself with "almost a serene deportment" despite their attempts to publicly humiliate her, and she will not allow the townspeople to see her shame. While the other women are proud in a domineering and unkind sort of way, Hester is proud in a quiet and self-respecting kind of way. The narrator even compares her to "the image of Divine Maternity," or the Virgin Mary, as she is "so picturesque in her attire and mien" with her baby on her arm. The Puritans hated Catholics, and Mary, mother of Jesus, is especially revered in the Catholic Church. Thus, in addition to making Hester more beautiful and dignified than her Puritan peers, he also connects her to a figure that would have reminded them of the group they hate the most.