And only recently I’ve thought that in SW, Vader answers to Tarkin, In ESB, EVERYONE answers to Vader, and in Jedi, Vader answers to the Emperor. Just something that crossed my mind.
I think the comparison isn’t completely fair between the films. In SW Tarkin and Vader seem to be friends who respect each other but Tarkin is the military boss who is in charge of the station. Also Vader doesn’t have much to do really on his own.
In TESB we see Vader only in his own SSD that is in charge of the relatively small fleet. Even then, the admiral of the fleet is in charge of the fleet, but sure, they act on Vader’s orders which is to find Luke and the rebels. So he had is own quest to complete by any means necessary. I think after the small group of rebels destroyed the Death Star, the Emperor realized the danger and Vader got a bit of a promotion. Before that Vader had served his duty by killing the Jedi already.