Of course the answer to this question is "neither" if she must be only one or the other. In one way, Hester Prynne in Nathaniel Hawthorne's The Scarlet Letter is a much less complicated character than her lover because her great sin is known to all and how she deals with it is overt; however, because of that public punishment, Hester does not have to deal with the effects of her sin on her soul in the same way that Arthur Dimmesdale must.
If a sinner is defined simply as someone who has sinned, then Hester is, indeed, a sinner. If we think of a sinner as being someone who persists in committing the same sin--then I might make the case that Hester is a sinner. The truth is that Hester is really only sorry for getting caught, which she does because she is pregnant. Her sin was not getting pregnant, though; her sin was loving a man who was not her husband while she was married. Thus the scarlet "A" for adultery emblazoned on her breast. True repentance requires a turning away from the sin, and while Hester is not with Arthur physically, she has not stopped loving him. In fact, when she get the chance, she commits to leaving Salem with him. She makes no apology for loving him even though she knows it is a sin.
Her attitude about sin and repentance is clear from this statement she makes to Dimmesdale in the forest:
"You wrong yourself in this," said Hester gently. "You have deeply and sorely repented. Your sin is left behind you, in the days long past. Your present life is not less holy, in very truth, than it seems in people's eyes. Is there no reality in the penitence thus sealed and witnessed by good works? And wherefore should it not bring you peace?"
When repentance is defined this way, as doing good works to compensate for one's wrongs, perhaps Hester is no longer a sinner; however, it is a wretched faith which requires only doing good but not changing one's heart in order to achieve true repentance.
In terms of being a saint, Hester could be considered one only in terms of her charitable acts in town. While these are saintly actions, they do not make Hester a saint and more than my making a basket on the basketball court makes me an NBA All-Star. We have to take her in totality, and Hester certainly exhibits some less-than-saintly behaviors at times. For example, she is afraid to pray because she is afraid her hatred for the cruel women in town will turn her prayers to curses. She also hates Roger Chillingworth for what he has done to Arthur, though of course Chillingworth forgave her of a great sin. These are not the thoughts and attitudes of a true saint.
In short, Hester is just a human being, struggling with sin and occasionally achieving saintliness. That is all of us, it seems to me; we do the lofty and right thing sometimes, but we certainly wallow is sin just as often. Hester is a strong woman to endure such public humiliation, to help even those who have scorned her, and to stand by Arthur despite everything; while these things do not make her a complete saint, they certainly keep her from being an abject sinner.