The encounter between Abigail and Danforth could be described as a power struggle of sorts.  Abigail clearly enjoys the power that her participation in the trials has conferred upon her, and Danforth, as the deputy governor of the province, already has a great deal of power that he'd surely like to retain.  When he asks her to consider that "the spirits [she has] seen are illusion only, some deception that may cross [her] mind [...]," she is instantly offended, despite the fact that she is lying.  She wants to be known as a martyr, not a liar, and she responds,

I have been hurt, Mr. Danforth; I have seen my blood runnin' out!  I have been near to murdered every day because I done my duty pointing out the Devil's people - and this is my reward?

Abigail claims that she is the victim, of course, that she is only trying to do what she knows to be right in pointing out witches who are hurting people.  In the face of her righteous anger, Danforth "weaken[s]" and tries to say that he doesn't "mistrust" Abigail, but she continues "in an open threat" to him,

Let you beware, Mr. Danforth.  Think you to be so mighty that the power of Hell may not turn your wits?  Beware of it!

Now, Abigail actually threatens the deputy governor of the Massachusetts Bay Colony, an incredibly dangerous thing to do in any other scenario, but here, now, she seems to imply that she could cry out on him next, that she could actually accuse him.  She then deflects attention away from any doubts about herself by accusing Mary Warren of sending out a "cold wind" in the courtroom.  This distracts everyone from the idea that Abigail and the other girls are lying, and she has put Danforth in his place: she is in control. 

In this way, Abigail seems to "win."  She has made the deputy governor, a powerful man, quail before her, and she has redirected the proceedings to benefit herself. 

In the confrontation between Abigail and Danforth in The Crucible, who "wins"?

The conflict between Abigail and Danforth is one in which he tries to assert control, establishing himself as the central driving force of authority.  Being very big on power and manipulation herself, she will not be cornered by anyone.  Her attempt to walk out of the courtroom and her ability to control the situation by feigning victimization is how Abigail is able to reassert control from Danforth.  She claims that she is not going to tolerate being questioned, viewing it as an insult.  Her act of walking out of the courtroom, being insulted and acting as a victim causes Danforth to bend and seeks to placate her.  In doing so, he gives her total authority, almost as if to validate her as an authority figure in her own right.  It is here in which Abigail wins the confrontation between she and Danforth.  It is a victory in which Abigail has managed to manipulate the situation, yet again, to her advantage.  It is also a moment in which Proctor recognizes that she does win and Abigail is on the warpath, a condition in which she has managed to win over everyone in Salem.  It is a situation in which Proctor recognizes the magnitude of the force he is up against when he sees that even Danforth has to acquiesce to Abigail.