1 hour ago, Forresto said:Tarkin is very clearly more powerful then simply his ranks and titles imply. The way ive always seen him is that he is the Emperor's real right hand man whereas Vader is simply an enforcer.
Tarkin is the kind of man that builds and maintains empires. He is administrator, soldier, and politician but he doesnt wish to be emperor. Tarkin is in charge of Vader because it is most likely Tarkin above all other men that the Emperor actually trusts.
In the Tarkin novel, it speaks of "The Emperor, Tarkin, and Vader: the Empire's newly formed dark triumvirate" right before the Emperor tells Tarkin about his Grand Moff title.
In the Star Wars Rebels: Visual Guide: Epic Battles book, it says "Except for Tarkin, Vader commands all the Emperor's servants" - and apparently the Lords of the Sith book confirms Vader as second in command of the Imperial Military with the Emperor as its head:
http://starwars.wikia.com/wiki/Imperial_Military
I would suggest that while Vader and Tarkin cannot give one another orders (Moffs seem to be in a slightly different chain of command parallel to the military) Tarkin can give almost anyone below Vader, orders.