Darth Vader vs Yoda

As the author of the "Most Helpful" response in the Kit Fisto Round I thread, this battle is seriously close, and I don't think anyone is going to present firm evidence that clearly favors either one. If I had to say anything, I would say ROTS Anakin > AOTC/ROTS Yoda > OT Vader > AOTC Anakin > OT Yoda. First of all, when you say "Darth Vader" it connotes black-suit with emphysema, but technically yellow-eye Anakin is also Lord Vader, and Anakin is at his very most powerful during the events of ROTS. Force abilities are directly related to how much biotic matter you have, so he was weakened by the events on Mustafar for sure. The answer to your question depends on whether we're talking ROTS "Lord Vader" or emphysema Vader.

Yoda has some excellent feats. He clearly has the advantage over Darth Tyrannus/Dooku in lightsaber combat. The AOTC script includes:

"YODA doesn't budge an inch. For the first part of the contest, he parries every cut and thrust that Dooku aims. Nothing the great swordsman tries gets through. His energy drains. His strokes become feebler, slower. YODA attacks! He flies forward. COUNT DOOKU is forced to retreat. Words are insufficient to describe the range and skill of Yoda's speed and swordplay. His lightsaber his a humming blur of light. Count Dooku's lightsaber is sent cartwheeling from his hand. He staggers back, gasping and spent, against the control panel. YODA jumps onto DOOKU'S shoulders, and is about to drive the lightsaber into the top of the Count's head."

The only reason Dooku ultimately escapes is because he takes advantage of Yoda's adherence to the Jedi Code when he threatens Obi-Wan and Anakin with being crushed by debris. Had Yoda not focused on saving Anakin and Obi-Wan, Dooku would have been unable to escape and would have perished.

In ROTS, Yoda clearly bests Darth Sidious according to the script, although I admit that the impression on a movie-viewer would be less favorable to the green sage. The ROTS script says:

"YODA unleashes a ferocious assault on PALPATINE, causing him to almost go over the edge. The Dark Lord drops his lightsaber but recovers with a BLAST OF ENERGY from his hands that surrounds YODA. YODA is deflecting the Sith Lord's lightning bolts. The energy bolts begin to arc back on the Emperor. It looks as if the Dark Lord is doomed."

Yoda ultimately flees the battle, not because he is a worse fighter, but because he knows that the clone army is after him, and he must prioritize his survival and the survival of the order. If he were able to deliver a decapitating strike to the Empire by offing Sidious, great, but otherwise the galaxy was too dangerous, and he needed to flee to the Sith stronghold of Dagobah where he would go undetected.

Unlike Yoda, Anakin actually kills Dooku. Dooku tries to do the "debris on Obi-Wan" trick again, and he still fails. In this moment, Anakin shows that he has surpassed Yoda, and these narrative choices are very deliberate. My only problem with Anakin is that his battle mastery tends to come from surprise rather than purely dominating. When Yoda fights, he fights (Dooku and Sidious are pure combat). When Anakin wins, he wins because of surprise (Windu and Ep. VI Sidious). When he dukes it out, the results are mixed (win against Dooku, lava against Obi-Wan in Ep. III). In terms of raw fighting skill, we've never seen AOTC/ROTS Yoda bested. In terms of the movie narrative, I think Lucas was very on the nose that Anakin succeeded where Yoda had not (he kills Dooku and brings balance to the Force in VI). Very tight, and don't let anyone tell you otherwise.