Lucas implies on the DVD and Blu commentaries that Vader is a subordinate in SW. Tarkin is the only person to give Vader orders beside the Emperor. Leia also throws out the insult that he is "holding Vader's leash".

Even pre-CW I thought they had an interesting relationship and probably a long working history together. Vader doesn't converse with any other Imperials that way in the rest of the OT.

Tarkin seems to respect Vader's abilities more than a certain General Motti does!

One of my favorite Marvel comic issues involves the Death Star's successor, (yes, they beat ROTJ to that idea!) and it's named the Tarkin. A secret group of high ranking Imperial officers have had enough of Vader throttling their peers left and right, and try to assassinate Vader by opening an airlock on the station. That would have made one heck of a scene in the movies!