In what ways has Abigail won in her emotional battle with John?
This answer is certainly dependent on your location in the book. Overall, Abigail is upset with John in Act I because he cut off their relationship. As she tries to get him to continue the adulterous relationship in secret, he refuses. This infuriates her and spurs the actions that ensure in Acts II and III. As Abigail has successfully caused division between John and Elizabeth in Act II, she begins winning an emotional battle with him because if she can't have him, I think she believes that no one else should... including his wife. By Act III, Abigail gets both Elizabeth and eventually John jailed. Now, she has complete control of the town. I believe this makes her feel emotionally superior. But by Act IV, she has to flee the town for fear that the truth which contradicts her lies may surface.
Her biggest battle won occurs in Act II when she achieves further dividing John and Elizabeth without even being in the room or in relationship with John.