5 REASONS IT IS BARRISS...
WHO INFILTRATED THE PRISON ?
1. When Tarkin is walking with Anakin and Ahsoka, Barriss looks nervous, when Tarkin explains the prisoner is going to be moved from the Jedi Temple to a new prison facility. This gave Barriss a heads up on Letta's whereabouts. Barris realized at that moment she will need to figure out a way to break in. Why ? Because Letta would sooner or later snitch. To avoid this, Barriss went into the prison with the intentions of killing Letta. It would of been easier killing Letta inside the Jedi Temple, but Tarkin threw a monkey wrench in her plan and now Barriss needed to move quickly.
WHO DROPPED THE KEY CARD ?
2. After killing Letta in a rather sloppy manner, Barriss realized she would need to get the attention off her. Many people wouldn't believe Ahsoka would murder someone. So Barriss needed to find a way to change people's minds. Barriss would assist Ahsoka in escaping and use her as a smoke screen to get the attention off her. Barriss would drop the keycard, and kill the guards framing Ahsoka.
WHY HELP AHSOKA ?
3. Realizing that Ahsoka proved far more difficult to capture then she originally thought, Barriss needed to find a way to continually keep the attention off her and on Ahsoka. She would lead her to the nanodroids, and then lead security forces to the area so that the link between the nanodroids and Ahsoka was made. So even if Ahsoka escaped, she would never be able to clear her name.
HOW IS BARRISS SO OVERPOWERED ?
4. First off, Barriss is not overpowered, but what makes you think Barriss is weak ?
Barriss is in the same age group as Ahsoka, and in a lot of ways far more mentally focused. Barriss at one point, "memorized all 200 junctions of a Geonosis hive, because her master told her too". Ahsoka doesn't have that type of focus and would of laughed in Anakin's face if he asked her to do it.
Having the mental fortitude to study a lightsaber style, and practice again and again and again and again, is not something that really is hard for a person like Barriss.
But can she beat Ahsoka in a duel ? Yes. ABSOLUTELY ! Why ? Because to kick ***** as a Jedi, has nothing to do with physical ability. It has to do with your level of focus. Clearing your mind, concentrating, and having the confidence to follow through. Three things that Ahsoka is not able to do at the moment.
Barriss was rested, focused, and ready to do what needed to be done.
Ahsoka was tired, scared, confused, or as she puts it, "Off her game.." because of the stress she was under.
Barriss, being the more disciplined one, made the decision early on that she would have to be ready to kill clones, frame friends, and tarnish the name of the Jedi forever in order to win. Ahsoka is still trying to wrap her head around the first one.
WHY DID BARRISS GO TO THE DARKSIDE ?
5. A bit of foreshadowing was mentioned in "Sabotage", that all Jedi have political ideals and see the Jedi Order involved in the war in a lot of different ways.
For Barriss, she hates the idea that the Jedi are involved in the war. She feels that the Clone Wars is hurting the reputation of the Order, and that the Jedi are losing their focus as peace keepers. Barriss, like Anakin, and Tarkin believe that the Jedi are not able to do what needs to be done to end the war because of their principles.
With no end to the war, Barris goal is simple.
To make the Senate and the Republic believe that the Jedi Order should be removed from Military Actions. With the Jedi Order removed from power, the Republic can take the gloves off and end the war. That sounds a lot like Tarkin, and that's because it is. However Tarkin and Barriss are not working together, and have completely different goals. Tarkin wants to consolidate all power underneath him and get the Jedi out of his territory, because he enjoys being in charge.
Barriss doesn't want power or to be in charge. She just wants the Jedi to go back to their roots as peace keepers and pacifists, and not be involved in Republic politics and military matters.
To do that, she will become focused and do whatever it takes to win.