A lot of fun speculation in this thread. There have been so many changes as the SW canon has expanded in terms of Vader's position. Remember, it is entirely possible that Vader was originally intended as one of many Sith Lords in service to the Empire. As late as the 90s Lucas was okay with the idea of the Emperor having other darkside users in his service

But when watching SW77, it is clear that both Tarkin and Vader are given relatively equal weight as the main antagonists. Their exact place within the Empire is interesting. Vader's power seems to be very much in the vein of how Mara Jade is later depicted by Zahn; a special envoy of the Emperor who has power and authority only at the behest of the Emperor. Tarkin has traditional authority via his position as a Governor, but is also a "Grand Moff" and had been granted (from the Emperor) widespread dictatorial power over a vast amount of territory in order to suppress dissidents. Tarkin is very similar to certain figures in Roman history in this respect.