Which, getting back on topic, is about Vader being under "Tarkin's leash".
I suspect that this mostly has to do with vader.
He's burned, scarred, not physically what he was. He's lost his wife, his kid(s), and he hasn't grown in the Force.
He is responsible for the deaths of all the Jedi, and wishes he hadn't done it. He clings on to his anger and hate, but in a hollow, depressed way.
I think the reason that he comes alive in ESB is mostly due to the fact that he knows Luke is alive.
He's got his son back, part of Padme, part of him. It's like the fire that was laying dormant was stoked, and he goes off.
Plus, the Death Star project was Tarkin's baby, and so while Vader didn't take any shit from the other generals, he would still be under Tarkin's command.
Plus, he argues with him anyway: "I told you she would never conciously betray the rebellion."
"I must face him... alone!"
I always felt that they were equals, they were just on Tarkin's turf.