Throughout most of the original Star Wars trilogy, Darth Vader seems to have complete control over the Empire's military hierarchy. It seems his only limitation is needing to report to his Sith Master, the Emperor. For example:
He has full command of the Imperial fleet in The Empire Strikes Back. He even summarily executes Admiral Ozzel and promotes a Captain (Piett) to take his place, without anyone questioning him.
(also in The Empire Strikes Back) After Captain Needa loses track of the Millenium Falcon, he honorably confesses to Lord Vader and is nevertheless executed in the same way.
There is one major exception: Grand Moff Tarkin, the commander of the original Death Star, seems to be superior to Darth Vader.
While choking an Imperial officer, Tarkin says "Vader, release him!" and Vader complies.
After the Millenium Falcon escapes, we learn that it was let go intentionally. Tarkin says "You're sure the homing device is secure aboard their ship? I'm taking an awful risk, Vader. This had better work." This attitude clearly implies that Tarkin some sort of superiority over Vader.
When he discovers the Princess Leia lied about the location of the Rebel Base, Tarkin tells Vader to "Terminate her... immediately." Although the Princess isn't actually executed, Tarkin's instructions are followed at least to the point of her being scheduled for execution. (C3PO says "I'm afraid she's scheduled to be terminated.")
Does Darth Vader have a military rank? If so, what is it?
If Vader does have a rank, is it lower than "Grand Moff" (Tarkin's title), or is it just subservient to the "Commander of the Death Star?"
Or does Darth Vader simply have a personal respect for Tarkin that leads him to follow his orders by choice rather than by obligation?