No, according to the book Dark Lord: The Rise of Darth Vader Tarkin does not outrank Vader. Vader mentions that Tarkin and other Moffs have been newly ranked as Moffs. That title is new. But Vader out ranks everyone except the Emperor. One admiral once called Vader, Admiral Vader. Vader ignored this. According to the book, Vader answers directly to the Emperor. I hope I answered your question.
The above answer is incorrect, Tarkin did indeed outrank Vader, as he was clearly giving him the orders in Episode IV, and did outrank everyone save Emperor Palpatine. After Tarkin dies aboard the first Death Star, Darth Vader is the one that is second in command, as evidenced in Episode V & VI by the fact that it was he who gave orders and impose authority over the imperial forces. The only thing i can say about the book Dark Lord, that says otherwise, is that it is non-canon, or that that at first Tarkin responded to Vader and later the other way around, as the movies answer for themselfs and don't need expanded universe to enforce the fact that it was Tarkin the one second in command in Episode IV.
Vader's rank and authority is similar to a Political Officer or Commissar in the Soviet Union in around 1940s. Commissars are special officers attached to an army corps or smaller squads to ensure their loyalty to Stalin, they have no official rank and usually follows orders given by the corps' current commanding officer. However, they have ultimate authority to field-execute the ocommanding officer or just simply take the commandship of the corp from the commanding officer himself if he committed either treason, disobedience to the USSR even if they are really high-ranked like a General of Admiral or something. If you see them that way, technically Commissars outranks all other officers but in reality, Commissars have no actual commandship at all and they are simply viewed as overseers. Vader is similar to that, he is simply attached to the Death Star to supervise and oversee the Death Star and represents the Emperor himself, he may have no actual military commandship but he is the Emperor's voice and apprentice
Perfect explination above. . You basically have to look at it as vader is an embassary of the emperor. His authority is given by the emperor to speak for him when needed, not necessarily as a military leader.. more like a one man special ops..