I think a key point is in SW how Vader's subordinated treat him. While he's plainly the boss, they aren't afraid of him and are free to disagree and almost argue.

By ESB Vader's moved up in the world. He has a bigger ship, commands other ships, and NO ONE gives him instructions and you question him at your peril.

How much of this can be accounted by a change in Vader the person, and how much can be accounted by a change in Imperial power structure?

One possibility is that his discovery of having a son (and planning a father/son coup) has made him more motivated/aggressive.

The other possibility is that Vader's now "off the leash." He's plainly been promoted, either because of the power vacuum above him after the DS went boom, or because his apparent mandate of hunting down the Rebels has now become the main focus of the Imperial navy.

Since Vader had a rise in status between SW and Empire, what does this tell us about his relationship with Tarkin?

In SW when Vader choked the douchebag in the confrence scene, everyone is shocked and appalled. Plainly this isn't normal... the dude pushed Vader a little too hard. After Star Wars, everyone almost expects to be choked... even Moff Jerjerood in ROTJ. This seems to indicate that Vader wasn't in a position to go around choking people willy-nilly in SW and one is left to wonder what would have followed if he hadn't obeyed Tarkin's order to release him.